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This paper proposes the hierarchical stability conditions for linear systems with an interval time-varying delay. In the matter of the delay, the upper and lower bounds are restricted, but there is no constraint on its derivative. Firstly, based on the state vectors and multiple integral state vectors involved in the delay-related generalized free-matrix-based integral inequalities (GFIIs), the hierarchical Lyapunov-Krasovskii functional (LKF) candidates are constructed. Then, the GFIIs are applied for the approximation of the integral quadratic terms, which will introduce the delay related nonlinear terms in the LKF differential. Next, the novel adjusted matrix-valued high and odd degree polynomial negative definite conditions (NDCs) are provided to acquire the hierarchical linear matrix inequality (LMI) conditions and cope with the nonlinear terms introduced by the GFIIs. Eventually, the advantages of the obtained stability conditions are checked through some numeric examples. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of achieving consensus in leader-following multi-agent systems under event-triggered control, with considerations of model uncertainties, network time-delay, and random deception attacks. To address the challenges of limited network resources, we propose a novel event-triggered control scheme that employs a dynamic memory-based approach. The proposed scheme utilizes multiple historic event-triggered states that are correlated with the states of neighboring agents and the leader, and the threshold parameter varies dynamically with time. We establish a memory-based closed-loop system that considers both network delays and deception attacks. Using the Lyapunov stability theory, a sufficient condition is derived to ensure consensus performance, and the desired controller gains and triggered matrices are obtained by solving linear matrix inequalities. Besides, we provide a comparative analysis of the memoryless dynamic event-triggered control. Finally, we validate the effectiveness of proposed approach with simulation results. [ABSTRACT FROM AUTHOR]

This paper studies the dynamic output feedback (OF) control problem for unmanned aerial vehicles (UAVs) with limited network bandwidth by a genetic-algorithm-assisted design approach. In order to make full use of the limited network bandwidth, only partial measurement information is transmitted to the controller via the sensor-to-controller network. Round-Robin protocol is introduced to administrate the transmission rule. Sufficient conditions are presented to make sure that the closed-loop UAV system is exponentially stable with the required L 2 -gain performance. However, due to the nonlinear coupling terms of the dynamic OF controller parameters and some redundant variables in the system modeling, the established conditions are non-convex and difficult to be solved. Fortunately, genetic algorithms (GA) show good performance in solving optimization problem with nonlinear and non-convex constraints. Therefore, this paper skillfully combines GA with linear matrix inequality techniques to solve the established conditions. Finally, all the dynamic OF controller parameters and the minimal L 2 -gain can be obtained simultaneously. At the end of this paper, an UAV networked control example and a numerical example are performed to verify the effectiveness and superiorities of our method. [ABSTRACT FROM AUTHOR]

This paper investigates the design problem of event-triggered ultimately bounded filter for two-dimensional discrete systems with time-varying delays subject to hybrid cyber-attacks. A bi-directional time-sequence event-triggered transmission scheme is developed under hybrid cyber-attacks to lighten the load of network bandwidth while preserving a satisfactory filtering performance. The impact of hybrid cyber-attacks, which occur in random patterns, on the filtering performance is also taken into account. In such a framework, an augmented system model accounting for the simultaneous presence of hybrid cyber-attacks and event-triggered transmission mechanism is established with respect to two-dimensional shift-varying discrete systems with time-varying delays. On the basis of the augmented model, sufficient conditions ensuring dynamic filtering error systems exponentially ultimately bounded in the mean-square sense are obtained in virtue of Lyapunov stability theory and the linear matrix inequality technique. Then, the asymptotic upper bound of the dynamic filtering error can be specifically quantified in terms of noise variance and cyber-attacks intensity. Furthermore, criteria for simultaneously designing the weighting matrix of event-triggered scheme and the filter gain matrix are derived by minimizing the asymptotic upper bound of filtering error. Finally, the validity of proposed ultimately bounded filtering algorithm is demonstrated by utilizing an example of the industrial heating exchange process. [ABSTRACT FROM AUTHOR]

The paper delves into the intricate details of unbiased H ∞ filtering for 2-D Markov jump systems with general transition probabilities in the light of the Roesser model. In order to allow the Markov jump systems to better model practical engineering applications, general transition probabilities are introduced. These probabilities are more flexible, encompassing all unknown, all known, and partially unknown cases to improve their practical applicability. The goal of this study is to showcase a novel unbiased filter to make the filtering error system mean-square asymptotically stable and meet a specified H ∞ disturbance attenuation performance. By constructing the Lyapunov function, sufficient condition for the corresponding filter to exist and the solutions of its parameters are given through linear matrix inequalities. Eventually, the Darboux equation is used to prove the utility of the presented filter. [ABSTRACT FROM AUTHOR]

This paper proposes a novel procedure for discretizing uncertain time-invariant continuous-time linear systems in polytopic domains. The approach is based on multistep method theory and involves mixing models obtained with different multiples of a fixed step-size (sampling time), thereby increasing data availability. An optimization procedure is employed to determine the coefficients that minimize the residual discretization error, and then these coefficients are combined to construct an augmented structure for the discrete-time system. The discretization error is computed using a grid search and incorporated into the discrete-time system formulation. Using the resulting discrete-time system, a state feedback methodology is applied to synthesize digital controllers capable of stabilizing the original continuous-time system. The paper presents two sufficient Linear Matrix Inequality (LMI)-based conditions for designing robust controllers specific to the proposed structure. The first condition utilizes a constant Lyapunov function, while the second condition employs a parameter-dependent Lyapunov function. In both cases, the proposed conditions guarantee asymptotic stability for the continuous-time system in closed-loop. A numerical experiment is conducted to illustrate the validity and effectiveness of the proposed method. • Discretizatizing continuous-time time-invariant uncertain systems is an open problem. • Considering delayed steps in the discretization can provide more information. • Suitable discrete-time control design procedures are presented. [ABSTRACT FROM AUTHOR]

This paper presents the problem of reachable set controller design for a class of nonlinear Markov jump cyber–physical systems (MJCPSs). The adverse effects of bounded peak external disturbances, uncertainties and false data injection (FDI) attacks with certain probability on MJCPSs are considered. The aim is to design an appropriate controller to guarantee that the actual state of the closed-loop MJCPSs is defined by a specified set. Firstly, the Lyapunov functional method is introduced because the time-varying delays are carried by FDI attacks. By using the Lyapunov functional method, an ellipsoid description of the reachable set containing all the states of the system originating from the origin is obtained. Then, the controller gain can be obtained via a set of feasible linear matrix inequalities (LMIs). Finally, the effectiveness of the designed reachable set controller is proved by simulation results. [ABSTRACT FROM AUTHOR]

In addition to meal intake, a diabetes system has a feedback behavior to balance the constituents of the chemicals, which causes instability. Therefore, a search for a feedback system that can stabilize the system with the introduced disturbances is a concern. In this article, a technique to stabilize a closed-loop system that considers the time-varying delay and rejecting disturbances is introduced. The closed-loop stability technique is designed and analyzed based on a selected suitable Lyapunov–Krasovskii functional (LKF) and satisfying the H ∞ performance, and the integral part is upper bounded by a reciprocally convex inequality approach. The optimal closed-loop controller gain is obtained from the feasibility of the linear matrix inequality (LMI) by considering the minimum of the H ∞ norm bound. To check the ability and performance of the proposed technique for the stability study, it is numerically applied to govern the blood glucose concentration of a 70 kg male patient co-experiencing both types (type 1 and 2) diabetes upon periodically glucose intake as external disturbances. The experiencing of the hybrid diabetes is achieved by varying the beta-cell functioning in insulin production. The proposed technique is able to stabilize and maintain the desired blood glucose concentration being inside a normal healthy range with both glucagon–glycogen conversion and insulin secretion delays. [ABSTRACT FROM AUTHOR]

The problem of reachable set estimation for singularly perturbed systems with time-varying delays and bounded perturbation is studied in this paper. Firstly, a Lyapunov–Krasovskii function related to the perturbed parameter η is established. Secondly, introducing a method of integral inequality scaling and eliminated the influence of singularly perturbed parameter on the system within a certain range. The system state is therefore contained in a η -independent ellipsoid in accordance with a criterion imposed by linear matrix inequalities. Subsequently, examples are used to show that the findings are valid. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the combined dissipativity state estimation criteria for memristor neural networks (MNNs) with additive and leaky time delays. The upper bounds of the Lyapunov–Krasovskii functionals (LKFs) are estimated using second-order Bessel–Legendre inequality (SOBLI) and improved reciprocally convex inequality (IRCI) approaches, and novel estimation criteria in the form of linear matrix inequalities (LMIs) are established. As a consequence, unique delayed-dependent criteria are developed to ensure that the estimated error MNN is dissipative. Finally, a couple of simulation examples are illustrated to explore the benefits and merits of the proposed methodology. One of these examples is supported by a realistic example to show a steady state response in the sense that it is asymptotically stable and well trackable for flux-charge domain (FCD) applications in energy storage systems; as a result, all currents, power, and voltages in the networks disappear, while the memristors function as nonvolatile memory, holding the outcome of a calculation, i.e., the asymptotic estimates of flux. The generalized dissipativity state estimation technique covers variations in the stability of various classes of delayed MNNs, as well as possible benefits over classic NNs working in the conventional FCD. • As a first attempt, a unified dissipativity index was used on MNNs with time delays. • A simple LMI constraint is established to investigate the state estimation problems. • The simulation study was presented to show the benefits of the suggested method. • Different from existing works, the FCD application was explored using the MNN model. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic output-feedback control for networked control systems (NCSs). The data transmissions in the sensor-to-controller and the controller-to-actuator channels are generated by the dynamic periodic event-triggering mechanism. Due to the existence of time-varying delays in the two channels, the updated data is received after a time delay. To cope with this problem, a hybrid dynamical framework of the NCSs is established. With the help of Lyapunov function-based approach, a new event-triggering condition is designed and sufficient conditions on input-to-state stability are derived. By introducing an auxiliary function, the obtained sufficient conditions are transformed into linear matrix inequalities and the explicit forms of the dynamic output-feedback controller gains are provided. Moreover, the upper bounds on the maximum allowable transfer intervals and the maximum allowable delays are derived. Finally, a numerical example illustrates the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamic event-triggered control problem for a networked Markovian jump system under hybrid attacks. In the concerned system, both the sensor-controller (S-C) network and the controller-actuator (C-A) network suffer from hybrid attacks, including denial-of-service (DoS) attacks and deception attacks. Two dynamic event-triggers at the controller and the sensor are designed to handle these dual-network hybrid attacks. Moreover, a unified framework is constructed to design an observer-based output feedback controller (OBOFC) which simultaneously considers hybrid attacks and dynamic event-triggering strategies (DETSs). Sufficient conditions to ensure the input-to-state stability (ISS) of the concerned system are derived. Furthermore, a set of linear matrix inequalities (LMIs) are proposed to obtain the desired observer-based feedback control gains and event-triggering parameters. A simulation example is given to further verify the effectiveness of the proposed control and event-triggered schemes. • A general model whose S-C and C-A networks suffer from both deception and DoS attacks • Two dynamic event-triggers to reduce the frequency of transmissions • A general ISS analysis framework based on a set of LMIs [ABSTRACT FROM AUTHOR]

The problem of finite-time state estimation is discussed for discrete singular Markov jump network systems (DSMNSs) based on event-triggered (ET) quantization control strategy. According to the ET network communication and quantization control schemes, an augmented DSMNS model with time-delays is first constructed. Employing stochastic Lyapunov functional and introducing relaxation matrix variables, sufficient conditions are established for the DSMNS to be singularly stochastic finite-time bounded. Besides, the ET gain matrices and ET quantized feedback controllers are co-designed by decoupling matrix variable parameters so that the augmented DSMNS is singularly stochastic finite-time bounded with a specified performance index. Eventually, the effectiveness of the proposed scheme is verified and evaluated by a numerical simulation. • The event-triggered quantized finite-time state estimation is investigated for DSMNSs with interval time-varying delays. • The finite-time event-triggered quantized state estimators and event-triggered gain matrices are co-designed to ensure the stochastic finite-time H ∞ boundedness of the DSMNS model in terms of separation matrix variables and linear matrix inequalities. • The effectiveness of the proposed approaches is verified by an electrical circuit example. [ABSTRACT FROM AUTHOR]

This article presents a new technique for suboptimal consensus protocol design for a class of multiagent systems. The proposed technique is based upon the extension of newly developed sufficient conditions for suboptimal linear–quadratic optimal control design, which are derived in this paper by an explication of a noniterative solution technique of the infinite-horizon linear quadratic regulation problem in Krotov framework. For suboptimal consensus protocol design, the structural requirements on the overall feedback gain matrix, which are inherently imposed by agents dynamics and their interaction topology, are recast on a specific matrix introduced in a suitably formulated convex optimization problem. As a result, preassigning the identical feedback gain matrices to a network of homogeneous agents, which act on the relative state variables with respect to their neighbors is not required. The suboptimality of the computed control laws is quantified by implicitly deriving an upper bound on the cost in terms of the solution of a convex optimization problem and initial conditions of the agents instead of specifying it a priori. Numerical examples are provided to demonstrate the implementation of proposed approaches and their comparison with existing methods in the literature. [ABSTRACT FROM AUTHOR]

In the paper, the global exponential stability for impulsive delayed Clifford-valued coupled neural networks is studied. Firstly, a delayed Clifford-valued coupled neural network model is established. So as to avoid the non-commutativity issue of Clifford numbers multiplication, the original n -dimensional Clifford-valued models are decomposed into 2 m n -dimensional real-valued models. Then, by using Lyapunov-Krasovskii (L-K) functional approach and the technique about linear matrix inequality, some new sufficient conditions are presented for the global exponential stability of the considered neural network models. Finally, the effectiveness of the results are verified by two numerical simulations. [ABSTRACT FROM AUTHOR]

This paper addresses the integral sliding mode control (ISMC) problem of uncertain impulsive systems with delayed impulses. Firstly, an integral sliding surface with embedded impulse information is constructed, which is able to counteract the intermittent impact of delayed impulses. Then an ISMC law is designed to guarantee the finite-time reachability of the predefined sliding surface without special restriction on system dynamics. Secondly, two different types of linear control laws with switching gains are proposed to robustly stabilize the sliding mode dynamics. The first type is independent of the size of impulse delays, and is used to tackle the impulses with unknown bounded delays. The second type aims at providing impulse-delay-dependent stabilization algorithms under the assumption that the delays are smaller than the impulse intervals. In the situation where the upper bounds of the uncertainties are characterized by two unknown constants, an adaptive ISMC law is proposed to ensure the existence of sliding mode. Switching Lyapunov functions and the state augmentation technique are introduced to exploit the positive/negative effects of delayed impulses. Several tractable conditions for designing the switching gains and the sliding surfaces are derived in terms of linear matrix inequalities. Finally, three numerical examples are presented to show the effectiveness of the proposed control algorithms and highlight their merits. [ABSTRACT FROM AUTHOR]

• The bio-economic SSMJSs is formulated using T-S fuzzy modeling, in which the commodity price is governed by a semi-Markov process, and an event-triggered controller is proposed for this system using an affine membership-based approach. • The required sufficient conditions to ensure the admissibility of the addressed system over a specified finite-time interval are obtained using dissipative theory and the Lyapunov-Krasovskii functional method. • The eel seedling harvesting model is used to demonstrate the effectiveness and utility of the developed controller design. An event-triggered scheme-based admissibilization problem of bio-economic singular semi-Markovian jump systems over a finite-time interval is investigated in this study, where the commodity price is assumed to follow a semi-Markov process. To facilitate analysis, the addressed system is expressed using Takagi-Sugeno fuzzy modeling with two fuzzy rules, which is then generalized to a finite number of fuzzy rules. Following that, an affine membership-based event-triggered controller is proposed for the system under consideration to ensure the desired admissibility within a given finite-time interval. A new set of conditions that adequately guarantees the aforementioned problem is derived using the Lyapunov-Krasovskii stability theory, parameterized linear matrix inequality technique and dissipative theory. A numerical example based on the eel seedling harvesting model is considered to validate the developed theoretical findings, where the significance of the proposed control design method is clearly demonstrated. [ABSTRACT FROM AUTHOR]

The robust H ∞ dynamic output feedback (DOF) control for a class of nonlinear time-varying delay rectangular descriptor Markov jump systems (DMJSs) is discussed in this paper, there are no restrictions on the rows and columns of the differential matrix E. The rectangular DOF controller is designed to make the closed-loop system as square DMJSs. Firstly, by utilizing a mode-dependent and delay-dependent Lyapunov-Krasovskii (L-K) functional and implicit function theorem, sufficient conditions are given to guarantee that the augmented closed-loop systems are robust stochastically admissible with an H ∞ performance and have unique solution simultaneously. Then based on certain matrix decoupling techniques, a new strict linear matrix inequality (LMI) sufficient condition for the existence of a rectangular DOF controller is obtained, and the controller is given. Finally, numerical examples are presented to verify the validity of the results. [ABSTRACT FROM AUTHOR]

• There is an uncomplicated nonlinear descriptor system for the lithium-ion battery, which does not involve additional derivation operations. • The nonlinear characteristics of the lithium-ion batteries are retained. Furthermore, the estimation accuracy of SOC is improved. • The dynamic characteristics of input current are preserved, which can significantly reduce the chattering caused by sudden current changes. • Fewer parameter adjustments bring a more convenient observer design process. • The proposed observer has excellent robustness and can deal with various uncertainties. A robust observer based on nonlinear descriptor systems is applied to estimate lithium-ion batteries' state of charge (SOC). We creatively take the relationship between the battery's open circuit voltage (OCV) and SOC as a nonlinear algebraic constraint, thereby modeling the battery as a nonlinear descriptor system. This model can effectively trade off accuracy and complexity. The robust convergence, even in the presence of uncertainties, is proven through a combination of the Lyapunov stability theorem and linear matrix inequality (LMI) techniques. Experimental results showcase the effectiveness of the proposed SOC estimation technique, offering enhanced convergence speed, estimation accuracy, and robustness compared to conventional sliding mode observers. [ABSTRACT FROM AUTHOR]

This paper investigates the composite anti-disturbance control problem for the interconnected Semi-Markovian systems with multiple disturbances and actuator faults, where the state signal of each subsystem is quantized by logarithmic quantizer before being transmitted into controller. Two representative types of external disturbances are considered simultaneously, one is norm-bounded and the other is formulated by an exogenous system. To attenuate the modelling disturbance and diagnose the actuator faults, a distributed disturbance observer with fault diagnosis observer is constructed. Then, the composite quantized control methodology is proposed to compensate disturbances and faults, and stabilize the overall system. On the basis of proper Semi-Markovian Lyapunov-Krasovskii functional, some sufficient criterions are derived to ensure the stochastic stability with a prescribed performance. Moreover, the desired observer and controller gain matrices can be attained via linear matrix inequalities (LMIs) technique. Finally, a simulation example is given to demonstrate the feasibility and effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

The article proposes a kind of stability analysis method for nonlinear time-delayed semi-Markov jump systems with incremental quadratic constraints. To meet the requirement of stochastic stability, the sufficient conditions formulated by linear matrix inequalities are derived. Both the transition rate of semi-Markov process and the time delay are time-varying, which make the considered system more general than the systems governed by Markov process and whose time delay is invariant. The mode-dependent Lyapunov-Krasovskii function is employed to analyze the stability problem. Besides, incremental quadratic constraints are proposed to reduce the conservatism of sufficient conditions. Finally, the effectiveness and superiority of the proposed method is verified by an example of virus mutation treatment model. [ABSTRACT FROM AUTHOR]

In this paper, the dissipativity-based asynchronous fault detection problem over unreliable communication is investigated for a class of Takagi-Sugeno fuzzy nonlinear Markov jump systems with time-varying delays and subject to uncertain probabilities. The communication links between the plant and filter are considered to be unreliable, where the stochastic quantization and measurement missing phenomenon are taken into account simultaneously. The asynchronization between the plant and the designed fault detection filter (the random quantizer), is modeled by independent hidden Markov models with a conditional probability matrix, where both the transition probabilities of the plant and the conditional probabilities of the filter are considered to be only partially accessible. By virtue of the Lyapunov stability theory and the slack matrix technique, sufficient conditions guaranteeing the resulting residual system being asymptotically mean square stable and strictly (Q , S , R)- α -dissipative are deduced. And then, the parameters of the desired fault detection filter are explicitly expressed by solving a set of strict linear matrix inequalities. Finally, two examples are utilized to demonstrate the effectiveness and practicability of the proposed design technique. [ABSTRACT FROM AUTHOR]

This paper considers the robust H ∞ guaranteed cost control problem for singular continuous-time semi-Markov jump systems. In quadratic cost function, the weighting matrices are indefinite. First, sufficient conditions are given which ensure the related closed-loop systems to be stochastically admissible with γ -disturbance attenuation, and the value of the cost function is bounded between zero and the positive upper bound. Then, by a new linear matrix inequality(LMI) method and a matrix decoupling technique, the reducible dynamic output feedback guaranteed cost controllers with full order or reduced order are designed. Last, the effectiveness of the proposed methods is illustrated by two examples. [ABSTRACT FROM AUTHOR]

In this study, we scrutinize the problems of resilient state tracking control (RSTC) and disturbance rejection (DR) for periodic piecewise polynomial delay systems in the presence of multiform disturbances and gain fluctuations. Specifically, we address both exosystem-induced disturbances and norm-bounded disturbances. Firstly, to tackle effectively the disturbances that are produced by exosystems, the disturbance observers are tailored, which estimates the disturbance in a precise manner. Secondly, the repercussions of norm-bounded disturbances can be lessened by accounting an extended dissipative performance. Moreover, by amalgamating the outcomes of the disturbance observer with the feedback-based tracking control, a DR-based RSTC is constructed. In addition, some parameter variations in the controller gain are taken into consideration in order to guarantee resiliency against unexpected flaws. Besides, the adequate conditions are derived in the form of linear matrix inequalities by making use of Lyapunov stability theory, new double integral inequality and extended Wirtinger's inequality. Furthermore, the relation for acquiring the controller and observer gain matrices is formulated based on the established criteria. Finally, a numerical example with simulation depiction is presented to show the favour performance and capability of the designed controller. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of sensor fault detection (FD) for discrete-time linear systems. First, considering the influence of disturbance, an adaptive law is designed based on the interval observer theory, which can effectively compress the error interval of output estimation, and improve the sensitivity to sudden faults. Then, based on adaptive interval observer (AIO), a flexible event-triggering fault detection mechanism is designed. Different from the existing methods, the event-triggering condition has greater flexibility. At the same time, the adaptive law can ensure that the zero signal belongs to the upper and lower bound of residual. Based on the robustness theory, the linear matrix inequality conditions (LMIs) satisfying the H ∞ performance index are derived. Finally, the effectiveness of the proposed method is demonstrated by an aeroengine simulation example. [ABSTRACT FROM AUTHOR]

In this paper, we aim to study model-based event-triggered control for a class of uncertain switched discrete-time systems composed of stabilizable and unstabilizable subsystems. A nominal model is introduced at the controller side to form a dynamic controller so that it can provide a kind of approximate estimate of the system state for system input even the overall switched discrete-time system is running in open-loop during any two consecutive event-triggered instants. By using multi-Lyapunov function method and the average dwell time switching strategy, stability conditions given in linear matrix inequality form for the closed-loop switched discrete-time system are derived. The design of control gains is also given. Finally, a numerical example and a physical example are provided to verify the effectiveness and usefulness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper deals with state estimation for a class of Lipschitz nonlinear systems under a time-varying disconnected communication network. A distributed observer consists of some local observers that are connected to each other through a communication network. We consider a situation where a communication network does not remain connected all the time, and the network may be caused by intermittent communication link failure. Moreover, each local observer has access to a local measurement, which may be insufficient to ensure the system's observability, but the collection of all measurements in the network ensures observability. In this condition, the purpose is to design a distributed observer where the estimated state vectors of all local observers converge to the state vector of the system asymptotically, while local observers exchange estimated state vectors through a communication network and use their local measurements. According to theoretical analysis, a nonlinear and a robust nonlinear distributed observer exist when in addition to the union of all communication topologies being strongly connected during a time interval, the component of each communication graph is also strongly connected during each subinterval. The existence conditions of the distributed observers are derived in terms of a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the presented method is numerically verified using some simulation examples. [ABSTRACT FROM AUTHOR]

The stability problem of fractional-order neural networks in consideration of time-varying delay is addressed by utilizing Lyapunov functional approach in this paper. Firstly, a class of novel Lyapunov-Krasovskii functions are designed to deal with the time-varying delay terms, which reduces the conservatism of the stability criteria. In addition, to estimate the fractional-order derivative of the Lyapunov-Krasovskii functions, a novel free-matrix-based fractional-order integral inequality is then established, which encompasses the Wirtinger one and leads to tractable linear matrix inequality criteria. Then, based on the designed adaptive control and the proposed Lyapunov-Krasovskii functions, some stability criteria depending on time-varying delay information and fractional-order α are deduced. Finally, numerical simulation shows that the presented approach can significantly reduce the conservatism of the existing results and has a broader application prospect. [ABSTRACT FROM AUTHOR]

Variable fractional-order (VFO) differential equations are a beneficial tool for describing the nonlinear behavior of complex dynamical phenomena. In comparison with the constant FO derivatives, it describes the memory properties of such systems that can vary in the time domain and spatial location. This article investigates the stability and stabilization of VFO neutral systems in the presence of time-varying structured uncertainties and time-varying delay. FO Lyapunov theorem is adopted to achieve order-dependent and delay-dependent criteria for both nominal and uncertain VFO neutral delay systems. The obtained conditions are given in respect of linear matrix inequality by designing a delayed state feedback controller. Simulations verify the main results. [ABSTRACT FROM AUTHOR]

In this paper, an observer with exponential time-varying gain is proposed for a class of nonlinear systems in Takagi–Sugeno form with both continuous-time and aperiodic sampled outputs. The proposed observer consists of two parts: one related to the continuous-time outputs and one related to the discrete outputs. Sufficient conditions involving a tuning parameter and the maximum allowed sampling time are derived in terms of quasi linear matrix inequality with respect to a scalar to ensure asymptotic convergence of the observer on the basis of Lyapunov–Krasovskii functional and H ∞ approach. Numerical simulations are provided to show the benefits of the proposed observer. Some comparisons with the high gain continuous-discrete observer and fuzzy observer with constant gain are provided to illustrate the interest of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the exponential stability of delayed neural networks (DNNs) with delayed sampled-data inputs is investigated via extended bilateral looped functional approach. Firstly, a new extended bilateral looped functional is constructed, which is differentiable at sampling intervals and can relax the constraints on positive definiteness when compared to traditional functionals. Then, less conservative criteria for exponential stability of DNNs with delayed sampled-data inputs expressed through linear matrix inequalities (LMIs) are obtained. Furthermore, the results are extended to T–S fuzzy DNNs with delayed sampled-data inputs, where corresponding stability conditions are likewise derived. Finally, two simulation examples are given to illustrate the validity of the main results. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of non-fragile guaranteed cost control (GCC) for networked nonlinear Markov jump systems subject to multiple cyber-attacks, which are characterized by Takagi–Sugeno (T–S) fuzzy model with time-varying delay. Specifically, a variety of cyber-attacks, including deception attacks and Denial-of-Service (DoS) attacks, are considered, which occur in the forward and feedback communication links, respectively. To achieve stochastic stability under guaranteed cost function (GCF), the paper proposes a Lyapunov–Krasovskii (L–K) function approach. The approach derives sufficient conditions for stochastic stability, and obtains non-fragile controller gains and the uniform upper bound of the GCF using linear matrix inequalities (LMIs) technique. Finally, the effectiveness of the proposed algorithm is evaluated by simulation experiment. [ABSTRACT FROM AUTHOR]

This article presents an H ∞ fuzzy dynamic observer-based dynamic sliding mode control (SMC) for continuous-time Takagi-Sugeno (T-S) fuzzy systems in the presence of external disturbances and uncertainties. Compared with the conventional SMC and the existing approaches, the effects of the unknown input signals whether linear or nonlinear are completely eliminated. Furthermore, the nonlinear systems which are modeled as T-S fuzzy systems are allowed to share different input matrices under the proposed SMC. The matrix gains of the proposed dynamic sliding surface are derived from the solution of the linear matrix inequalities (LMIs). In addition, an H ∞ fuzzy dynamic observer is proposed based on a new approach for T-S fuzzy systems affected by uncertainties and external disturbances. To reduce the analytical complexity and avoid the non-convex problem, a new transformation is used to propose both dynamic sliding surface and the dynamic observer. The stability conditions are extracted also in form of an optimization problem. Lastly, a Translational Oscillator with an eccentric Rotational proof mass Actuator (TORA) system is simulated with the proposed methods to show the superiority and effectiveness. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-time state estimation for neural networks under hybrid cyber-attacks based on adaptive event-triggered scheme (AETS). Firstly, Markov jump process is used to describe different types of cyber-attacks. In order to save communication resources, the system output state model under mixed cyber-attacks is established based on AETS. At the same time, a state estimator based on the output signal is designed to avoid the state unavailability of the system. By constructing a Lyapunov-Krasovskii functional and affine Bessel-Legendre inequality method, sufficient conditions are obtained to guarantee the estimation error system is finite-time boundedness and mixed passive and H ∞ performance level. The expected gain of the state estimator is obtained by solving a set of feasible linear matrix inequalities. Finally, the robustness and effectiveness of the proposed method are verified by three numerical examples such as Chua's circuit. [ABSTRACT FROM AUTHOR]

Limitations of the standard backstepping control technique are overcome in this paper by yielding global conditions for regional ones; specifically, flexible cascade arrangements that do not require the system to be put in a pure- or strict-feedback form to ensure controllability beforehand, handling of nonlinear MIMO blocks without invertible input distribution matrices, calculation of virtual and real control laws regardless of the non-affine-in-control nature of subsystems, and systematic numerical synthesis of Lyapunov-based control laws at each step of the cascade connection via linear matrix inequalities. All these benefits derive from exploiting exact convex rewriting of nonlinear terms, splitting available and non-available signals for control implementation, and applying the direct Lyapunov method to cast conditions as a convex optimization problem. Examples of academic and practical interest illustrate the advantages of the novel methodology over former approaches. [ABSTRACT FROM AUTHOR]

This paper focuses on the stability problem and the design method of PI-type H ∞ controller for load frequency control (LFC) of power systems with multiple time-varying delays (MTD). In the existing researches, the model of LFC system with time delays is not accurate enough since it is established based on the assumption that the time delays are all the same. This paper proposes a novel model of multi-area LFC system with MTD. Both the stability analysis and controller design in this paper are based on the improved model to ensure the applicability of the proposed method in general. First, a novel Lyapunov-Krasovskii functional (LKF) containing delay-product-type term (DPT) is constructed and auxiliary function-based integral inequality (AFBII) is utilized to handle the integral term of the derivative of LKF. Then, an improved reciprocally convex inequality is proposed to obtain the less conservative stability criteria in terms of linear matrix inequalities (LMIs). Next, an effective H ∞ controller design method is developed based on the proposed stability criteria. Finally, simulation experiments are done to illustrate the superiority of proposed criteria and effectiveness of proposed design method. [ABSTRACT FROM AUTHOR]

For nonlinear space-varying parabolic distributed parameter systems, this paper introduces an H ∞ fuzzy intermittent boundary control, where the output measurements are only available at some specified boundary position (i.e., boundary measurements). Initially, a Takagi–Sugeno fuzzy parabolic partial differential equation is used to precisely describe the nonlinear space-varying parabolic distributed parameter system. Then, under boundary measurements, an H ∞ fuzzy intermittent boundary control design based on the Takagi–Sugeno fuzzy parabolic partial differential equation model ensuring the exponential stability with an H ∞ performance for closed-loop space-varying distributed parameter system is subsequently obtained via spatial linear matrix inequalities by employing inequality techniques and piecewise switching-time-dependent Lyapunov function. Furthermore, in order to solve the H ∞ fuzzy intermittent boundary controller design of nonlinear space-varying parabolic distributed parameter systems under boundary measurements, we express spatial linear matrix inequalities as linear matrix inequalities and further present some linear matrix inequality based fuzzy intermittent boundary control design conditions respecting the property of membership functions. Finally, two simulation examples are offered to demonstrate the effectiveness of the proposed H ∞ fuzzy intermittent boundary control method. [ABSTRACT FROM AUTHOR]

This paper studies the robust stabilization problem of a class of uncertain Lipschitz nonlinear systems with infinite distributed input delays. A novel robust predictor feedback controller is developed and the controller gain can be obtained via solving a linear matrix inequality. It is shown that the proposed robust predictor feedback controller can globally exponentially stabilize the concerned uncertain nonlinear system with infinite distributed input delays. The key to the proposed approach is the development of several new quadratic Lyapunov functionals. The obtained results are extended to the case of systems with both multiple constant input delays and infinite distributed input delays. It is noted that the obtained results include some existing results on systems with constant input delays or bounded distributed input delays as special cases. Finally, two examples of Chua's circuit and spacecraft rendezvous system are presented to illustrate the effectiveness of the proposed robust controllers. [ABSTRACT FROM AUTHOR]

This paper is devoted to the stochastic H ∞ control of uncertain delayed neutral semi-Markovian jumping systems subject to fractional Brownian motions (fBms) with H ∈ (1 2 , 1). Firstly, a novel Lyapunov–Krasovskii functional (LKF) with exponential terms is constructed. Secondly, by means of leveraging the derivation rule, Wirtinger inequality, Schur complement and linear matrix inequalities (LMIs), stability analysis and controller gains are retrieved. Finally, through a simulation example, the control scheme is validated to be reasonable and effective. [ABSTRACT FROM AUTHOR]

This paper studies the aperiodic sampled-data control problem of singular Markov jump systems under uncertain and unknown transition rates. First, taking into account the system information from x (t k) to x (t k + 1) , a novel two-sided looped mode-dependent Lyapunov–Krasovskii function (LKF) is constructed, which provides more freedom to test the feasibility of the LMI condition in the criterion. Based on this LKF and an improved integral inequality, a stochastic admissibility condition is given by linear matrix inequalities (LMIs), which is less conservative. Then, by using a lemma of equivalent set, a controller algorithm without equality constraint is proposed by LMIs to ensure the stability of the system. Finally, several examples are provided to verify the validity of the main results. [ABSTRACT FROM AUTHOR]

The issue of non-fragile controller's designed with reachable set estimation and time-delay for multi-agent systems(MASs) is investigated in this paper. The information interaction among agents is governed by a set of switching sequence, which can be described by continue-time discrete state semi-Markov process. By tree-transformation, the MASs firstly converted into reduced-order system, and properly considered the instability of the parameters with the dynamic behavior of the controller, a non-fragile controller is designed to describe the system's performance cope with the perturbation from the controller. The sufficient conditions are established in forms of a series of linear matrix inequalities which are based on Lyapunov-Krasovskii method, and the agent's state of error systems is bounded by a finite closed set will be guaranteed. Finally, the availability of the derived theoretical results are verified by two numerical simulations. [ABSTRACT FROM AUTHOR]

As for the multi-agent systems (MASs) with time-varying switching subject to deception attacks, the leader-following consensus problem is studied in this article. The one-sided Lipschitz (OSL) condition is utilized for the nonlinear functions, which makes the results more general and relaxed than those obtained by Lipschitz condition. The nonidentical double event-triggering mechanisms (ETMs) are adopted for only a fraction of agents, and each agent transmits the data according to its own necessity. Semi-Markov process modeling with time-varying switching probability is adopted for switching topology and deception attacks occurring in transmission channel are considered. By using the cumulative distribution function (CDF) and the linear matrix inequality (LMI) technology, sufficient conditions for MASs to achieve consensus in mean square are obtained. An effective algorithm is presented to obtain the event-based control gains. The merits of the proposed control scheme are demonstrated via a simulation example. [ABSTRACT FROM AUTHOR]

• The bumpless transfer problem for switched linear systems under the bump induced event-triggered mechanism is considered. • A novel event-triggered mechanism with controller bump is proposed, which can avoid Zeno behavior. • The provided bumpless transfer control method does not require triggering at the switching points. • By the multiple Lyapunov functions method, a switching law, the controller and the event-triggered scheme are co-designed. Event-triggered control with bumpless transfer for a class of switched linear systems is investigated. The description of event-triggered bumpless transfer (ETBT) performance can restrict the bumpy amplitude at both switching and triggering moments. In order to restrict the bump of the controller with event-triggering, we propose a novel event-triggered mechanism depending on the control bump. A positive lower bound on the event-triggering intervals is estimated. By using multiple Lyapunov functions (MLFs) approach, a sufficient condition is obtained to ensure global asymptotical stability and bumpless transfer performance for switched linear systems with bumpless transfer induced event-triggered strategy. The controller for subsystems, the switching law and the event-triggered scheme are simultaneously acquired by solving linear matrix inequalities (LMIs). Finally, the validity of the designed approach is confirmed through a switched RLC circuit and a numerical example. [ABSTRACT FROM AUTHOR]

This paper investigates the slow state variable feedback control issue for a group of singularly perturbed Markov jump systems with time-varying state delay in the discrete-time domain. The primary goal of this paper is to propose a slow state controller design approach that ensures the closed-loop dynamics attain stochastic stability with an H ∞ performance. First, the time-varying delay is introduced into system state and Markov jump chain is employed to depict system topological change. Secondly, by resorting to the Lyapunov functional theory and matrix analysis method, several necessary criteria are provided to guarantee the desired control performance. The derived conditions rely not only on the size of time-varying state delay and the upper bound of the singular perturbation parameter, but also on the order of the generated Markov jump mode sequence. Based on the established conditions, the gains of the desired slow state controller are obtained by means of the feasibility of a set of linear matrix inequalities. Eventually, a numerical simulation and a tunnel diode circuit model are presented to demonstrate the efficiency of the proposed technique. [ABSTRACT FROM AUTHOR]

This paper provides a new non-quadratic stabilization conditions based on adaptive fuzzy observer for a class of Takagi-Sugeno (T-S) fuzzy systems subject to external disturbances and both actuator faults and saturation. Firstly, an observer based fault tolerant control (FTC) is proposed, not only to estimate both system states and actuator faults but also to compensate for the actuator faults and to stabilize the faulty system with input constraints. The saturation effect is transformed into dead-zone nonlinearity and the generalized sector bound condition is used to estimate the attraction domain. To less the conservatism of the quadratic Lyapunov technique, a proper integral structure based on the non-quadratic function is investigated. The H ∞ criteria is considered and the robust stabilization conditions of the faulty closed-loop system are expressed as a linear matrix inequalities (LMIs) optimization problem. Finally, the robustness and the advantages of the proposed approach are demonstrated through a mixed CSTR and a numerical example. [ABSTRACT FROM AUTHOR]

• A general proportional integral observer - based disturbance compensation framework is constructed, using the idea of two-degree-of-freedom design, to achieve compensation for local disturbances and state-consensus control of wireless sensor network systems. • A minimum variance controller based on LMI solving is designed to achieve state consensus control for the complex sensor networks. • The design of the disturbance compensation uses the idea of zero-pole optimization to achieve feedback disturbance rejection control for periodic disturbances, providing a new solution for the handling of periodic disturbances. [Display omitted] Precise time synchronization is an enabling technology for mission-critical time-sensitive Industrial Internet of Things (IIoT). However, the crystal oscillator clock which is widely used in IIoT may suffer from periodic disturbances caused by repetitive motion or periodic vibration. To improve the time synchronization of distributed nodes subject to periodic disturbances, this paper proposes a novel disturbance rejection framework, General-Proportional-Integral-Observer-based Disturbance Compensation (GPIO-DC), with the proof of stability, and combined with a 2-freedom control design strategy to optimize both the disturbance rejection and clock tracking performance. And the GPIO's unique feature of blocking zeros are fully exploited to reject the periodic disturbance at its frequencies and a zero-pole optimal design algorithm is given. With the disturbance being compensated, a disturbance-free minimum variance time synchronization protocol for a complex network is developed and optimized by using Linear Matrix Inequality (LMI) to minimize the variance of networked synchronization errors. The performance of the proposed method is devalued by intensive simulation. Comparing with recent relevant research, the proposed method achieves a better performance in disturbance rejection and minimum variance. [ABSTRACT FROM AUTHOR]

• This proposal as a first attempt to inspect the extended dissipativity index of OSJPs under self-excited nonlinear wave force and structured uncertainty via DPIC technique. • More generalized integral inequalities are used in combination to improve the system stability of the OSJPs, and a comparison results also were employed along with existing work in the literature. • A novel set of required suppositions in terms of LMIs are offered using Lyapunov stability analysis and the DPIC technique to ensure the robust asymptotic stability of OSJPs with optimized attenuator γ. • To demonstrate the efficiency and generalizability of the suggested control, it was compared to existing research in the literature. This paper addresses the challenge of delayed proportional integral control (DPIC) of an offshore steel jacket platform (OSJP) subjected to a self-excited nonlinear wave force and structural uncertainty using the unified criteria. By introducing discrete and distributed state delays in the control input, a DPIC was established to stabilize the OSJPs. The goal of this study is to design a proper controller that will stabilize the dynamic of an OSJP while subjected to structural uncertainty and nonlinear wave force. The OSJP is investigated as a nonlinear dynamics with mixed state delays, allowing us to study its robust asymptotic stability using the Lyapunov-Krasovskii function (LKF) in the context of the extended dissipativity performance index. A novel closed-loop system-based stability criterion is derived as a result of using tighter integral inequalities to estimate the upper bounds of the delay and influential control gains can be achieved if a set of linear matrix inequalities (LMIs) is checked by simulation results, that the proposed control scheme can significantly improve the control's performance. Finally, it was demonstrated that the proposed control approach is more effective and multi-dynamic performances have been illustrated through the comparisons to previously published results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the leader-following consensus issue is investigated for a class of nonlinear multi-agent systems with semi-Markov parameters subject to hybrid cyber-attacks. A semi-Markov chain is adopted to describe the variation of switching topologies caused by the complexity of the environment and makes the studied problem more general. Hybrid cyber-attacks consisting of denial-of-service attacks and deception attacks are described with the help of two groups of Bernoulli sequences which are assumed to be independent of each other. On this basis, a sufficient condition for the stability of the consensus error system is established by using linear matrix inequality techniques. Finally, the validity of the results obtained is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the sampled-data master-slave synchronization problem for chaotic neural networks with actuator saturation by constructing novel Lyapunov-Krasovskii functionals. The proposed functionals exploit the sampling interval from the recent sampling instant t k to the next sampling instant t k + 1 by using the integral vectors ∫ t k t e (s) d s , 2 t − t k ∫ t k t ∫ t k s e (u) d u d s , ∫ t t k + 1 e (s) d s , and 2 t k + 1 − t ∫ t t k + 1 ∫ s t k + 1 e (u) d u d s. Based on the proposed functionals, this paper derives sufficient criteria for the sampled-data master-slave synchronization of chaotic neural networks with actuator saturation represented using a dead zone nonlinearity. Also, the controller gain matrix of the sampled-data controller can be obtained by solving linear matrix inequalities (LMIs). The superiority and validity of the proposed criterion are verified through the numerical example obtained from the literature. [ABSTRACT FROM AUTHOR]

This paper concentrates on the distributed consensus control of heterogeneous fractional-order multi-agent systems (FO-MAS) with interval uncertainties. Unlike previous methods, no restrictive assumptions are considered on the fractional-orders of the agents and they can have non-identical fractional-orders. Therefore, the closed-loop system becomes an incommensurate fractional-order system and its stability analysis is not easy. It makes consensus control more challenging. To design a systematic controller, new Lyapunov-based Linear Matrix Inequality (LMI) conditions are proposed which are suitable to determine the state feedback controller gains. Then, the consensus of heterogeneous fractional-order agents with an observer-based controller is provided. Finally, some numerical examples are provided to verify the effectiveness of our results. [ABSTRACT FROM AUTHOR]