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An innovative technique for developing fuzzy preview tracking control nonlinear systems using Takagi‐Sugeno (T‐S) fuzzy models is discussed. The design considers robustness against state time‐changing latency, input saturation, and reference tracking. To achieve this, the T‐S fuzzy system was combined with time‐changing latency and input saturation to create an augmented error system, transforming the original fuzzy preview tracking control issue into a stability issue for the augmented error systems. Next, a new fuzzy preview tracking controller was developed by considering the T‐S fuzzy systems' states or outputs, a distinct integrator, and a previewed reference signal to solve the tracking control issue. For the augmented error system's asymptotic stability, new adequate conditions were derived by employing the fuzzy Lyapunov function, small gain theory, and linear matrix inequality (LMI) method. Finally, the proposed method's effectiveness was demonstrated using two numerical examples. [ABSTRACT FROM AUTHOR]

In this paper, we provide a dissipative Hamiltonian (DH) characterization for the set of matrices whose eigenvalues belong to a given LMI region. This characterization is a generalization of that of Choudhary et al. (Numer. Linear Algebra Appl, 2020) to any LMI region. It can be used in various contexts, which we illustrate on the nearest Ω-stable matrix problem: given an LMI region $ \Omega \subseteq {\mathbb C} $ Ω ⊆ C and a matrix $ A \in {\mathbb R}^{n \times n} $ A ∈ R n × n , find the nearest matrix to A whose eigenvalues belong to Ω. Finally, we generalize our characterization to more general regions that can be expressed using LMIs involving complex matrices. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates anti‐attack stabilization with passivity problem of uncertain singular semi‐Markov jump systems (singular S‐MJSs) with exogenous disturbance and delay. An ingenious non‐fragile observer‐based neural sliding mode control (SMC) scheme is put forward to solve the problem. First, considering unmeasured states, a distinctive non‐fragile and decoupled observer, which does not contain the control input or any auxiliary sliding mode compensator design as in existing observer‐based SMC approaches, is established such that the disadvantages of sliding mode switching in observers in existing literature can be avoided. Then, “only one sliding surface” design and a new system analysis route are presented, and the derived sliding surface is accessibly designed. Next, a new version of stochastic admissibility and passivity sufficient condition is given, and a related algorithm via an optimization problem is proposed to determine the controller gain and the observer gain by linear matrix inequalities (LMIs). Further, a novel observer‐based anti‐attack neural SMC law, which utilizes a neural network‐based approach to approximate actuator attack, is proposed to stabilize the singular S‐MJSs against actuator attack. Finally, simulation and comparison results are presented, which demonstrate the effectiveness and superiority of our method. [ABSTRACT FROM AUTHOR]

In this article, we address the topics of fault reconstruction and robust fault‐tolerant tracking control for periodic piecewise polynomial uncertain systems with time‐varying delays, faults and external disturbances. In detail, the periodic piecewise polynomial learning observer system is configured with the intent to concurrently reconstruct the faults and immeasurable states of the system that is being considered. Precisely, the key intent of this study centers around in devising a robust fault‐tolerant tracking control to achieve the tracking performance of the system as intended with mixed H∞$$ {H}_{\infty } $$ and passivity performance. To this end, a robust fault‐tolerant tracking control is designed by incorporating the reconstructed faults and error feedback, which aids in vouching for the outcomes that were desired. Besides, by building the periodic piecewise polynomial Lyapunov–Krasovskii functional and making use of the matrix polynomial lemma and Wirtinger's inequality, certain adequate conditions are procured in the frame of linear matrix inequalities. Subsequently, the required gain values for the devised controller and the configured observer are found by using the established linear matrix inequalities. Ultimately, in order to attest the controller's intrinsic potential and relevance, numerical example along with the simulation results is supplied. [ABSTRACT FROM AUTHOR]

To address the issue of poor robustness in the model predictive control of grid‐connected inverters due to disturbances in load model parameters, this article developed an ultra‐local model robust predictive controller based on Linear Matrix Inequality (LMI). First, to avoid dependence on model parameters, an ultra‐local model of the system was constructed. Second, in the process of setting the state variable compensation gain, to simplify the complex computational steps of the traditional Lyapunov algorithm, the task of finding the gain that satisfies the Lyapunov stability condition was ingeniously transformed into an optimization problem of solving constrained LMI. Third, the optimized state variables are utilized to design a new cost function predictive model, thereby enhancing the precision of system control. Finally, the effectiveness of the proposed approach has been validated through simulations and experiments. [ABSTRACT FROM AUTHOR]

This paper addresses the H ∞ filtering problem for mean field stochastic differential systems that involve both state-dependent and disturbance-dependent noise. We assume that the state as well as the measurement output is distracted by an uncertain exogenous disturbance. Firstly, a sufficient condition for the stochastic-bounded real lemma is given. Next, H ∞ filtering, which is built upon a stochastic-bounded real lemma, is put forward by two linear matrix inequalities. Furthermore, the validation of the theoretical analysis is demonstrated with two examples. [ABSTRACT FROM AUTHOR]

Summary: The thesis studies a stochastic H∞$$ {H}_{\infty } $$ finite‐time bounded (SH∞$$ {H}_{\infty } $$FTB) filter design method for time‐varying delay Markov jump systems (MJSs) with partially unknown transition rates. First, a Lyapunov–Krasovskii functional with triple integral is built, the free weight matrix is added for lowering the conservatism. And the condition of SH∞$$ {H}_{\infty } $$FTB of the error system is analyzed. Then, according to linear matrix inequalities (LMIs), a new filter design method is presented. Moreover, the dimension of the filter obtained is free, and the filter ensures that the error system is SH∞$$ {H}_{\infty } $$FTB. Finally, the validity and effectiveness of the conclusion of this paper are demonstrated by simulation examples. [ABSTRACT FROM AUTHOR]

Under the influence of sensor saturation and packet dropout, this paper is concerned with the fault detection (FD) problem for a class of nonlinear systems with two additive time‐varying delay components. In the addressed measurement model, the sensor is assumed to have two communication channels, which can contribute to improving the probability of successfully delivering the measurements. A FD filter is designed to generate residual signals, and the sufficient criteria are established to ensure the stochastic finite‐time stability (SFTS) of the residual system with H∞$$ {H}_{\infty } $$ performance constraint by constructing new Lyapunov‐Krasovskii functionals. Based on the established criteria, the explicit expression of the desired FD filter is obtained via solving a set of linear matrix inequalities (LMIs). Finally, the usefulness of the proposed FD scheme is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the examination of global asymptotic stability pertaining to uncertain complex-valued stochastic neural networks (UCVSNNs) with multiple time delays. This paper employs the real-imaginary separated activation function to establish an equivalence between complex-valued neural networks (CVNNs) and two real-valued activation functions, representing the real and imaginary parts respectively. This equivalence is utilised to analyse the original UCVSNNs model in a comprehensive manner. The global asymptotic stability of the studied UCVSNNs model is ensured by constructing an appropriate Lyapunov-Krasovskii generalised function and applying the $ It\hat {o} $ It o ˆ formula, linear matrix inequality (LMI) and other analytical techniques to derive the system stability and other sufficient conditions. In the meanwhile, we provide two numerical examples to demonstrate the reliability and benefit of the discovered results. [ABSTRACT FROM AUTHOR]

In this paper, we explore a stabilisation problem for two different class of memductance functions for memristive bidirectional associative memory neural networks (MBAMNNs) with time-varying delay. A new Lyapunov-Krasovskii function (LKF) with double and triple integral terms is derived with some sufficient conditions to guarantee the global asymptotic stability criteria using the Lyapunov stability theory. The controller gain matrix for sampled-data controller is obtained for the state-dependent switched system and state-dependent continuous system in terms of linear matrix inequalities (LMIs). Finally, we stabilise the considered model by visualising the simulation part using standard MATLAB software which demonstrates the validness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, an interval multiobserver is designed for nonlinear systems subject to unknown but bounded disturbances and measurement noises. The behavior of discrete nonlinear systems is described by an uncoupled multimodel. Linear Matrix Inequalities (LMIs) are formulated to study the stability of the proposed systems and to ensure the cooperativity dynamic of the observation errors. An augmented system is introduced to apply a tracking control where the control gains are obtained by pole placement. Finally, a numerical example is proposed to verify the efficiency of the interval multiobserver in state estimation and to prove the performance of the control strategy to follow the desired trajectory. [ABSTRACT FROM AUTHOR]

Addressed in this paper is the reachable set estimation (RSE) problem for fuzzy‐model‐based leader‐follower multi‐agent systems with time‐varying delays and false data injection attacks. First, the aperiodic sampled‐data control is designed for the follower agents with randomly occurring false data injection attacks. Then, using the Kronecker product, the error system between the leader and the follower is obtained in a compact general form. Next, a novel Lyapunov‐Krasovskii functional is constructed with the knowledge of sampling patterns and time‐varying delays. In the framework of linear matrix inequalities, sufficient consensus conditions are determined from the H∞$H_\infty$ performance index and Lyapunov theory to guarantee that its reachable set is enclosed by an ellipsoid in the existence of bounded perturbations. In the end, the Duffing Van der Pol oscillator and the single‐link robot arm models are employed to validate the derived theoretical results. [ABSTRACT FROM AUTHOR]

This paper presents a fuzzy sliding mode control method for voltage control of islanded AC/DC hybrid microgrid. The T‐S fuzzy model is utilized to approximate initial non‐linear dynamic model of the microgrid. The fuzzy rules and membership functions are designed according to the coupling relationship between AC part and DC part. To reduce the influence of external disturbance and cyber‐attacks, an integral sliding mode controller is considered. Furthermore, a sufficient condition is proposed with H∞${H}_\infty $ attenuation performance to ensure the asymptotic stability of sliding motion. The set of gain matrices can be acquired via solving the linear matrix inequalities deduced from the Lyapunov stability analysis. The reachability to the proposed sliding mode surface can be guaranteed via switching control law based on a Lyapunov function. In addition, to eliminate chattering performance of the sliding mode control theory, the fuzzy logic controller is designed to optimize the switching region in boundary layers of saturation functions. Finally, the simulation results for the islanded AC/DC hybrid microgrid are implemented to verify the robustness and effectiveness of the designed fuzzy sliding mode control method. [ABSTRACT FROM AUTHOR]

This paper focuses on the exponential stability and the resilient state feedback controller design for large‐scale networked control systems under denial‐of‐service attacks. The duration of each denial‐of‐service attack is captured by a logical processor embedded in the controller. The closed‐loop system of periodic sampled‐data control is modelled as an aperiodic sampled‐data control system associated with lower and upper bounds on the duration of the denial‐of‐service attack. Two formal results are demonstrated. The first result is the stability criterion for large‐scale networked control systems under denial‐of‐service attacks obtained by constructing a two‐sided mode‐dependent loop‐based Lyapunov–Krasovskii functional under the action of a prediction‐based controller. The second result presents a criterion based on linear matrix inequalities to design the controller against denial‐of‐service attacks. In particular, iterative algorithms are given for computing the allowable delay upper bound for the system. Finally, the effectiveness of the proposed method is verified by the interconnected power systems of the two areas. [ABSTRACT FROM AUTHOR]

This work examines a polytope-type approach for observer-based security control of a fractional-order system that is under multiple attacks via an event-triggered scheme. A novel multiple-attack model is first proposed for fractional-order systems such as denial-of-service attacks and reply attacks, which can destroy the system's security during the signal process. In contrast to previous studies, the design of the controller is developed using an observer-based event-triggered scheme in the presence of multiple attacks. An event-triggering strategy is proposed to reduce the communication burden of the output measurement signals. An observer-based control is designed to keep the fractional-order system stable in all scenarios where one or more simultaneous attacks may occur. These findings can ensure the absence of Zeno behaviour and considerably reduce data transmissions. By employing the suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to ensure fractional-order system stability. Controller and observer-gain matrices are obtained by using the linear matrix inequality technique. Finally, two examples are provided to demonstrate the feasibility and usefulness of the suggested methodology. [ABSTRACT FROM AUTHOR]

In this paper, the energy-to-peak filtering problem for the uncertain discrete-time singular bilinear systems is studied. This paper considers the uncertainties that consist of real systems and the possible data packet dropouts when performance output signals and measurement output signals are transmitted over digital channels. In the course of the study, the phenomenon is elucidated utilising the Bernoulli random binomial distribution. The goal is to design the desired filter, so that the filtering error system is admissible, and meets the specified energy-to-peak performance index. The design conditions of energy-to-peak filters for uncertain discrete-time singular bilinear systems are given by introducing the Lyapunov function and using linear matrix inequalities (LMIs). The impact of uncertainty on singular bilinear systems is addressed using a two-step approach. At last, a numerical illustration is provided to demonstrate the validity of the design. [ABSTRACT FROM AUTHOR]

This paper is concerned with the event-triggered control problem for Roesser model-based two-dimensional (2D) Markov jump systems with multiple communication channels. In order to optimize the utilization of communication resources, an event-triggered rule (ETR) is proposed based on the structural characteristics of the 2D Markov jump plant. In addition, a stochastic communication protocol (SCP) is utilized to schedule transmissions from the controller to the actuators. Under the ETR and the SCP, an asynchronous state-feedback control scheme is formulated, allowing for mode mismatches between the controller and the 2D plant. A sufficient condition on both stochastic stability and a predefined H ∞ disturbance-attenuation performance of the closed-loop 2D system is established. Building upon this condition and linear matrix inequalities, a computationally efficient method is developed for designing the required state-feedback controller gains. Finally, the feasibility and effectiveness of the proposed event-triggered control approach are demonstrated by the application of a simulation example involving the Darboux equation. [ABSTRACT FROM AUTHOR]

This paper investigates the stabilization problem of interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy fractional order systems (FOSs). Firstly, IT2 fuzzy model is constructed to approximate the subject to actuator saturation of systems. Then, the sufficient conditions of output feedback control of IT2 fuzzy FOSs in terms of linear matrix inequalities (LMIs) are presented by using the method involving matrix singular value decomposition (SVD). Furthwemore, we solve optimization problems to estimate stable regions according to the proposed stability conditions. Finally, we proposed a numerical example to demonstrate the availability of theoretical analysis results. [ABSTRACT FROM AUTHOR]

The traditional Model Predictive Control (MPC) algorithm, grounded in precise mathematical models, faces challenges attributed to uncertainties in vehicle model parameters and modeling errors. These limitations result in suboptimal accuracy of the path tracking controller, particularly in complex driving environments. To address this issue, a tube-based model predictive control strategy (Tube MPC) is proposed. Initially, nominal dynamic modeling of intelligent vehicles is conducted, followed by linearized derivations. Leveraging the resulting linearized nominal model, the MPC cost function is solved to derive the control law for the nominal system. Subsequently, an error model between the actual and nominal systems is established, integrating various target constraints for path tracking and formulating a robust objective function. Utilizing the linear matrix inequality optimization method, a state feedback-assisted control law is derived to mitigate steady-state lateral position error. This approach ensures a more precise alignment between the actual and nominal states, ultimately enhancing tracking accuracy. Finally, experimental validations are conducted in the Carsim/Simulink simulation environment, encompassing diverse vehicle speed conditions and driving scenarios to assess the proposed controller against traditional Model Predictive Control. The experimental results demonstrate that, while ensuring vehicle stability, this control method exhibits superior tracking accuracy. [ABSTRACT FROM AUTHOR]

This work presents a contribution to reduce the conservatism in nonlinear observer for TakagiSugeno fuzzy systems with unmeasurable premise variables based on the mean value theorem. The conservatism was reduced through the use of non-quadratic Lyapunov function (NQLF) rather than the quadratic form used in previous works. The stability conditions are given in the form of Bilinear Matrix Inequalities (BMI) whereby an effective solution to solve this type of problem is presented using linear solvers which are characterized by their computational efficiency. To show the improvement of the proposed work over the existing approach and to demonstrate its effectiveness in solving the Bilinear Matrix Inequalities, the feasibility area is illustrated by a numerical example, and a real-time implementation of the observer is applied to the induction motor (IM) where a big number of inequalities is present. • Using the TS fuzzy model representation which obtained by using the non linear sector transformation. • Reducing the conservatism of the classical Mean Value Theorem observer by using the polyquadratic Lyapunov function. • Presenting an iterative linear matrix inequalities method to solve bilinear matrix inequalities using linear optimization solvers. • Real-time implementation of the proposed observer on an induction motor. [ABSTRACT FROM AUTHOR]

This paper introduces a fuzzy intermittent control issue for nonlinear PDE-ODE coupled system under spatially point measurements (SPMs), which can be represented by an ordinary differential equation (ODE) and a partial differential equation (PDE). Firstly, the nonlinear coupled system is aptly characterized by the Takagi–Sugeno (T–S) fuzzy PDE-ODE coupled model. Subsequently, based on T–S fuzzy model, a novel Lyapunov function (LF) is provided to design a fuzzy intermittent controller ensuring exponential stability of the closed-loop coupled system. The stabilization conditions are presented by means of a group of space-dependent linear matrix inequalities (SDLMIs). Finally, simulation results are given to illustrate the effectiveness of the proposed design method in the control of a hypersonic rocket car (HRC). [ABSTRACT FROM AUTHOR]

In this study, we investigate how natural environmental conditions affect a training vessel using a 'mathematical model of wind and wave' specific to Lake Silm near Kamionka, Poland. Wind and wave measurements on the lake were conducted. We present the vessel's trajectory under varying conditions: navigating in restricted waters simulating port conditions with speed readings, and during propeller operation. The control system of the nonlinear autonomous object employed two controllers: a linear matrix inequality controller and an overriding trajectory controller. We assess the impact of nonlinearities in the measured waves. It is shown that the maximum entropy probability distribution conforms more closely to the empirical frequency histogram than the Gaussian distribution. The wave height probability distributions diverge from Rayleigh distributions, indicating slight nonlinear effects. These results enhance the mathematical model of Silm Lake's wave dynamics. [ABSTRACT FROM AUTHOR]

The issue of state feedback sliding mode control (SMC) for a particular kind of active quarter-car suspension system is discussed in this work. The suspension systems' dynamic system is built with the three control objectives of maximal actuator control force, suspension deflection, and ride comfort in mind. The next step is to build the state-feedback controller with the disturbance (vibration) attenuation level in mind to guarantee the asymptotic stability of the closed-loop system. The algorithm for SMC design is introduced. It is predicated on choosing the sliding surface correctly using the invariant ellipsoid approach. The system motion in the sliding mode is guaranteed to be little affected by mismatched disturbances according to the control architecture. Furthermore, the presence of admissible controllers is articulated in terms of LMIs through the use of Lyapunov theory and the linear matrix inequality (LMI) technique. The objective is to create a desired dynamic state-feedback controller when these requirements are met. Lastly, a quarter-car model is used to illustrate how successful a suggested approach is. [ABSTRACT FROM AUTHOR]

As a giant in energy consumption, buildings urgently need to optimize control strategies for the main energy consuming equipment inside buildings. It is of great significance to design advanced control algorithms to improve the efficiency of the main energy consuming equipment in buildings, namely air conditioning, in the current energy shortage. The model predictive control algorithms and strategies were used in this study to control the HVAC system to improve the energy utilization of the city. Then linear matrix inequality with robust model predictive feedback controller was used to optimize and get the model predictive control optimization algorithm. The research results showed that, under the influence of different factors, the three regions controlled by the model predictive control optimization algorithm showed a little overshooting in the initial state. But it was quickly corrected after adjustment. Meanwhile, the average tracking error of temperature and humidity in each region was 0.139°C and 0.13g/kg dry air, respectively. The average predicted mean vote was 0.32. In actual office buildings, the proposed algorithm controlled the temperature within the reference value range of 0.1°C throughout the entire process. The total electricity consumption and electricity price costs were reduced by 12.11% and 22.54%, respectively. In summary, the proposed method has good performance for HVAC system application, which can effectively realize energy saving and emission reduction and improve human comfort. This method makes important contributions to promote the construction of smart cities and the development of green buildings. [ABSTRACT FROM AUTHOR]

This paper investigates the exponential stability in mean square sense for a class of stochastic switched semi‐Markov jump systems (ssSMJS). In this model, a hierarchical control switched regulation is designed, considering the external stochastic disturbances and generally uncertain transition rates (TRs) of the entire system and making the system more general and practical. By using appropriate Lyapunov–Krasovskii functional, linear matrix inequality, Jensen inequality, and mode‐dependent average dwell time (MDADT), sufficient conditions on the exponential stability in mean square sense for ssSMJS are derived. Furthermore, a nonfragile state feedback controller is designed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed criterion. [ABSTRACT FROM AUTHOR]

In this paper, a novel dynamic event‐triggered control protocol for leader‐following problems of generic linear multi‐agent systems is proposed. Compared with the existing static event‐triggered strategy, the developed event‐triggered approach significantly reduces the utilization of communication resources while guaranteeing asymptotic consensus, and the interevent time is adjustable. Under this event scheduling mechanism, a synthesis approach combining controller and observer design is presented. The observer‐based control and event‐triggered rules are distributed, which only require local information of each agent to implement. The proposed methods incorporate model‐based estimation and auxiliary dynamic variables with a clock‐like behavior to prolong the interevent time as long as possible. The sufficient conditions for leader‐following consensus are established using linear matrix inequalities (LMIs) formulation to facilitate numerical computation. Comparative simulations in different scenarios demonstrate the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the robust stability and stabilization problems of continuous‐discrete fractional‐order two‐dimensional Fornasini–Marchesini second model with interval uncertainties. Firstly, for the nominal model with fractional‐order α∈(0,2)$$ \alpha \in \left(0,2\right) $$, the unified LMI‐based stability conditions are presented by general description of stable root‐clustering sets. Secondly, these stability conditions are transformed to be more tractable for stabilization, and the LMI/BMI‐based stabilization conditions are established via state feedback controllers. Meanwhile, one algorithm is proposed to solve the BMI‐based conditions. Thirdly, facing interval uncertainties in this model, the LMI‐based robust stability conditions and LMI/BMI‐based robust stabilization conditions are established. Lastly, two examples are given to show the validity of our robust stability and stabilization results. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing event‐triggered H∞$$ {H}_{\infty } $$ state feedback controllers for uncertain fractional‐order systems subject to time‐varying delays. An event‐triggered H∞$$ {H}_{\infty } $$ controller is proposed based on an event‐triggered mechanism and the refined fractional‐order Razumikhin theorem. This controller guarantees the uniformly asymptotic stability of the controlled system while maintaining a predefined H∞$$ {H}_{\infty } $$ performance index. The uniformly asymptotic stability of the controlled system is understood that the zero solution of the uncertain fractional‐order time‐delay systems without external disturbance is uniformly asymptotically stable. The main difficulty of this problem lies in the memory and heritability characteristics of the fractional‐order calculus operator, particularly in the context of delayed fractional‐order systems, where preventing the occurrence of the Zeno phenomenon is paramount. The Zeno phenomenon exists when an infinite number of discrete transitions occur in a finite time interval. To overcome this difficulty, new event‐triggered H∞$$ {H}_{\infty } $$ state feedback controllers without Zeno behaviors are designed based on inequality techniques and several essential properties of fractional‐order calculus. Finally, the effectiveness and feasibility of the proposed method are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of two-dimensional (2D) system-based modified preview repetitive control (MPRC) with equivalent-input-disturbance (EID) for continuous-time systems. First, an EID-based MPRC law is used to improve the tracking performance and disturbance attenuation. Next, by using a new equality constraint, a continuous-discrete 2D system is established and the design problem of the EID-based MPRC law is transformed into the stability problem of the 2D system. Then, we employ the 2D system theory together with the linear matrix inequality (LMI) approach, a sufficient condition is derived to ensure the stability of the closed-loop system. By solving an LMI, the gains of the controller and state observer can be obtained. Finally, two numerical examples are provided to illustrate the effectiveness and superiority of the developed controller design technique. [ABSTRACT FROM AUTHOR]

ABSTRACT In this article, the reachable set estimation problems for a class of singular discrete‐time nonlinear systems (SDNS) with time‐varying delay (TVD) are presented. First, we employ a Lyapunov function scheme and utilize zero‐type free matrix equations. Based on this, a criterion is derived in the form of linear matrix inequalities (LMIs) to guarantee that the considered system to be regular, causal, and the state trajectory x1$$ {x}_1 $$ of the system is bounded. Second, by developing the singular systems decomposition technique into slow and fast subsystems and using the introduced auxiliary lemma, we establish that the x2$$ {x}_2 $$ state trajectory of the fast subsystem is also bounded, and the reachable set of singular nonlinear system is bounded within the ellipsoid. Finally, Numerical examples are presented to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT This article investigates the robust secure output tracking control for a class of uncertain two‐dimensional (2‐D) networked control systems. The 2‐D systems are described by the well‐known Fornasini–Marchesini (FM) local state‐space model, the parameter uncertainties are assumed to reside in a polytopic region, and the deception attacks are supposed to occur randomly in the transmission process. In the problem formulation, Bernoulli random variables are used to characterize the phenomena of deception attacks. As main results, a novel H∞$$ {H}_{\infty } $$ performance analysis condition for the augmented closed‐loop system is proposed by using a novel parameter‐dependent Lyapunov function and some zero equalities. Furthermore, both parameter‐dependent and parameter‐independent controllers have been designed, respectively, such that the output of the 2‐D systems tracks the output of a given reference model well in the H∞$$ {H}_{\infty } $$ sense. The design conditions are presented in terms of linear matrix inequalities (LMIs). In the end, a numerical simulation on a practical thermal process is applied to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Optimizing the performance of motion control systems with variations in nonlinear parameters is not an easy task. To accomplish this task, it is important to design the controller using the linear system approach. In this study, a linear parameter varying (LPV) control method is proposed in which nonlinearities are treated as parameter variations for planar motors. The proposed control method consists of the force and torque modulation with the commutation scheme and the nonlinear current controller with H∞ state feedback control in the form of LPV synthesis to improve the position-tracking performance. An interpolated gain-scheduling controller based on LPV synthesis is determined by applying H∞ control to a linear matrix inequality technique. An interpolated gain-scheduling controller can attenuate disturbance without disturbance estimation. The effectiveness of the proposed control method is evaluated using simulation results and compared with the conventional proportional–integral–derivative control to verify both improved position-tracking performance and disturbance attenuation. [ABSTRACT FROM AUTHOR]

This study focuses on examining the issues of extended dissipative-based composite anti-disturbance reliable tracking control for stochastic Takagi–Sugeno fuzzy systems afflicted by sensor faults and multiple disturbances. Explicitly, the multiple disturbances include the autonomous Wiener process and non random noises with partly known information that are generated by an exogenous plant. To address the difficulty of estimating the non random disturbance while considering the partially known information, the study incorporates a fuzzy stochastic disturbance observer. Furthermore, to solve the output tracking issue of the system under consideration, a modified repetitive tracking control is implemented. Then, combining the methodologies of disturbance observer-based control technique with modified repetitive control, a composite anti-disturbance reliable tracking control strategy is developed for achieving the intended tracking goal despite the multiple disturbances and sensor faults encountered. Additionally, the proposed approach involves extended dissipativity scheme, which includes $ H_\infty $ H∞, passivity, dissipativity, and $ \mathfrak {L}_2 - \mathfrak {L}_\infty $ L2−L∞ performances in a unified framework. In particular, by employing Lyapunov–Krasovskii functional approach, the essential stability criteria for the proposed closed-loop system are articulated in the form of linear matrix inequalities. Additionally, numerical illustrations are presented to exemplify the application and efficiency of the developed control protocol. [ABSTRACT FROM AUTHOR]

ABSTRACT This article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed. [ABSTRACT FROM AUTHOR]

This paper addresses the co-design of event-triggered dynamic output-feedback (DOF) control for discrete-time linear parameter-varying (LPV) systems. Two independent event-triggering schemes are introduced to determine when to transmit data from the sensor to the controller and from the controller to the actuator channels. Enhanced conditions employing linear matrix inequalities (LMIs) are derived to establish constructive criteria for simultaneously designing the gain-scheduled DOF controller and the triggering mechanisms, ensuring the asymptotic stability of the closed-loop LPV system's origin. Additionally, a convex optimisation problem is proposed to enlarge the inter-event sampling on the independent channels of sensor-to-controller and controller-to-actuator. Numerical examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

ABSTRACT In this article, new linear matrix inequality (LMI) conditions are proposed to guarantee robust stability of the closed‐loop of the linear time‐invariant one‐dimensional uncertain system by dealing with both continuous‐time (CT) and discrete‐time (DT) cases. These improved conditions for robust state feedback control combine the non‐monotonic approach and Finsler's technique. The benefit of the non‐monotonic approach returns to the utility of an arbitrary number of quadratic functions by considering the higher order derivatives of the vector field in the CT case (or the higher order differences of the vector field in the DT case). Finsler's technique aims to solve the closed‐loop stability problem in a larger parametric space. The strong points of the suggested LMI conditions are easy to program, eliminate the product between the state matrix and Lyapunov matrices, reduce the constraints by avoiding the decrease monotonically along trajectories for each quadratic Lyapunov function, guarantee the robust stability of the closed‐loop by using a state‐feedback gain. The simulation results show and confirm the effectiveness of these proposed conditions. [ABSTRACT FROM AUTHOR]

This paper focuses on the study of robust two-stage quadratic multiobjective optimization problems. We formulate new necessary and sufficient optimality conditions for a robust two-stage multiobjective optimization problem. The obtained optimality conditions are presented by means of linear matrix inequalities and thus they can be numerically validated by using a semidefinite programming problem. The proposed optimality conditions can be elaborated further as second-order conic expressions for robust two-stage quadratic multiobjective optimization problems with separable functions and ellipsoidal uncertainty sets. We also propose relaxation schemes for finding a (weak) efficient solution of the robust two-stage multiobjective problem by employing associated semidefinite programming or second-order cone programming relaxations. Moreover, numerical examples are given to demonstrate the solution variety of our flexible models and the numerical verifiability of the proposed schemes. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed robust frequency control (DRFC) scheme for industrial applications that can effectively adjust the frequency and regulate the active power-sharing ratio of islanded microgrids (MGs). The proposed method also enhances the H∞ performance and the transient response of the MGs by imposing pole placement constraints in the linear matrix inequality (LMI) framework. The proposed scheme utilizes the information on active power and frequency deviations of each distributed generator (DG) and its neighboring DGs to generate an auxiliary control signal implemented by the secondary control layer. The auxiliary control signal improves the input of the droop controller block at the primary control layer, ensuring both frequency regulation and proportional active power-sharing among the DGs. To show the robustness of this novel feature, an AC-islanded MG is simulated under various load and fault scenarios. The simulation results demonstrate the effectiveness and efficiency of the proposed scheme in stabilizing the frequency and damping ratio of the MG while maintaining an active power-sharing balance. [ABSTRACT FROM AUTHOR]

This paper explores the synchronization control issue for a class of fractional-order Complex-valued Neural Networks (FOCVNNs) with additive time-varying delays (TVDs) utilizing a sampled-data-based event-triggered mechanism (SDBETM). First, an innovative free-matrix-based fractional-order integral inequality (FMBFOII) and an improved fractional-order complex-valued integral inequality (FOCVII) are proposed, which are less conservative than the existing classical fractional-order integral inequality (FOII). Secondly, an SDBETM is inducted to conserve network resources. In addition, a novel Lyapunov–Krasovskii functional (LKF) enriched with additional information regarding the fractional-order derivative, additive TVDs, and triggering instants is constructed. Then, through the integration of the innovative FOCVII, LKF, SDBETM, and other analytical methodologies, we deduce two criteria in the form of linear matrix inequalities (LMIs) to ensure the synchronization of the master–slave FOCVNNs. Finally, numerical simulations are illustrated to confirm the validity of the proposed results. [ABSTRACT FROM AUTHOR]

In this paper, a new observer-based single-phase robustness sliding mode controller (SPRSMC) is proposed for the pitch control of a variable speed wind turbine (VSWT) systems. The finding of this research includes two tasks: i) to ensure a global stability of the VSWT plant, the reaching phase in traditional sliding mode control (TSMC) technique is eliminated and ii) to guess the immeasurable variables of VSWT plants, a novel pitch angle output feedback controller is constructed based on the estimator tool and output information only. Firstly, a single-phase switching function is determined to eject the reaching phase in TSMC. Moreover, an immeasurable variable of the VSWT system is estimated by employing the suggested estimator tool. Next, a SPRSMC for VSWT plant is built based on the support of the estimator instrument and output data only. Furthermore, an appropriate requirement is founded by utilizing the linear matrix inequality (LMI) method for ensuring the robust stability of motion dynamics in sliding mode. Finally, the solution of the suggested control is confirmed the three-blade wind turbine with a 5- MW utilizing the wind turbine simulator fatigue, aerodynamics, structures, and turbulence (FAST) code and the National Renewable Energy Laboratory (NREL). [ABSTRACT FROM AUTHOR]

This study treats the problem of Finite Time Stability Analysis (FTSA) and Finite Time Feedback Control (FTFC), using a Linear Matrix Inequalities Approach (LMIA). It specifically focuses on Takagi–Sugeno fuzzy Time Delay Fractional-Order Systems (TDFOS) that include nonlinear perturbations and interval Time Varying Delays (ITVDs). We consider the case of the Caputo Tempered Fractional Derivative (CTFD), which generalizes the Caputo Fractional Derivative (CFD). Two main results are presented: a two-step procedure is provided, followed by a more relaxed single-step procedure. Two examples are presented to show the reduction in conservatism achieved by the proposed methods. The first is a numerical example, while the second involves the FTFC of an inverted pendulum, which exhibits both symmetrical dynamics for small angular displacements and asymmetrical dynamics for larger deviations. [ABSTRACT FROM AUTHOR]

This paper introduces a sum-of-squares (S-O-S) approach to Stability Analysis and Stabilization (SAS) of nonlinear dynamical systems described by General Conformable Polynomial Fuzzy (GCPF) models with a time delay. First, we present GCPF models, which are more general compared to the widely recognized Takagi–Sugeno Fuzzy (T-SF) models. Then, we establish SAS conditions for these models using a Lyapunov–Krasovskii functional and the S-O-S approach, making the SAS conditions in this work less conservative than the Linear Matrix Inequalities (LMI)-based approach to the T-SF models. In addition, the SAS conditions are found by satisfying S-O-S conditions dependent on membership functions that are reliant on the polynomial fitting approximation algorithm. These S-O-S conditions can be solved numerically using the recently developed SOSTOOLS. To demonstrate the effectiveness and practicality of our approach, two numerical examples are provided to demonstrate the effectiveness and practicality of our approach. [ABSTRACT FROM AUTHOR]

This article addresses the static output feedback load frequency control (LFC) problem for semi‐Markov type interconnected multi‐area power systems (IMAPSs) through non‐fragile proportional‐integral (PI) strategy. Primarily, by roundly exploiting the dynamical properties and considering random mutations of the IMAPSs, the semi‐Markov jump process (MJP) is elaborately scheduled for establishing the dynamical model with precision. Subsequently, on account of the characteristic of geographical isolation, a memory‐like sampled‐data LFC mechanism considering time‐varying transmission delay for the semi‐Markov jump IMPASs is formulated accordingly. Additionally, the non‐fragile issue is explored for the PI controller gain fluctuations to meet the actual operation scenario. After that, a mode‐dependent two‐side polynomial‐type looped Lyapunov functional is constructed for enhancing flexibility. Then, in virtue of the stochastic analysis technique, some relaxed conditions guaranteeing stochastic stability with prescribed H∞$$ {H}_{\infty } $$ performance are thereby derived in the shape of linear matrix inequalities (LMIs). Ultimately, a numerical example is carried out to validate the efficacy of the developed control methodology. [ABSTRACT FROM AUTHOR]

This article addresses the problem of designing an event‐triggered fault detector within a networked nonlinear system described by a Takagi–Sugeno (T–S) fuzzy model, accounting for time‐varying delays and denial‐of‐service (DoS) attacks characterized by a binary Markov chain. Our focus is on constructing an event‐triggered residual system, which aims to detect malfunctions in the original fuzzy system while optimizing communication resource allocation. Specifically, it is tailored to combat DoS attacks in the event generator‐to‐fault detector channel and mitigate network‐induced time‐varying delays. Utilizing the Lyapunov–Krasovskii function approach, we formulate linear matrix inequalities to establish the necessary conditions ensuring the asymptotic mean‐square stability of the residual system, meeting a predefined H∞$$ {H}_{\infty } $$ performance criterion. Finally, the simulation results are presented to validate the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This article considers exponential stabilization (ES) of switched interval type‐2 (SIT2) fuzzy systems with asynchronous switching control. The SIT2 fuzzy system switches from one mode to another according to transition probabilities (TPs). A general SIT2 fuzzy quantized event‐triggered output controller (QETOC) is designed to save the communication resources. The QETOC employs distinctive membership functions from those of the IT2 fuzzy model and switches with mode‐pendent switching delay, which is more practical than asynchronously switched control techniques with a common switching delay and control schemes without TP. By designing discretized multiple Lyapunov function (DMLF) and using convex combination technique, sufficient conditions formulated by linear matrix inequalities (LMIs) are obtained to ensure that the DMLF does not 'jump high' at the moment of switching, and hence the conservatism of obtained results is significantly reduced since no additional dwell time is needed for the stabilization. It is discovered that the SIT2 fuzzy system is not necessary to be unstable on mismatched intervals, and it can be unstable on matched intervals. The advantages of theoretical analysis are verified by numerical simulations, and the classical assumption that each subsystem is unstable on mismatched intervals is conservative for control design. [ABSTRACT FROM AUTHOR]

Complex physical processes, which could evolve in both spatial and temporal dimensions and be represented by partial difference equations, could also operate in a repetitive mode with iterative learning methods as suitable control laws. For these three-dimensional systems (of the spatial, temporal, and iterative dimensions), the stability in the iterative direction is critical for many applications, which can be analyzed and synthesized under the proposed concept of iterative dissipativity. The definition of iterative dissipativity, which is first introduced in this paper, encapsulates the dominant information in both the spatial and temporal dimensions, while also placing a particular emphasis on the iteration improvement. This property allows for the derivation of sufficient conditions for asymptotic stability in the iteration direction, which are represented by linear matrix inequality criteria that can be readily solved. Performance in both the spatial and temporal dimensions can also be satisfied under this iterative dissipativity concept, even in absence of real-time feedback. Moreover, the optimization solutions of the control parameters can be determined. Finally, a thermal process and a numeric example are presented to illustrate the effectiveness of the proposed iteratively dissipative learning control approach. [ABSTRACT FROM AUTHOR]

Summary: In this article, the issue of resilient filtering for descriptor nonhomogeneous Markovian jump cyber‐physical systems under hybrid cyber‐attacks has been studied. First, occurrences of both deception attacks and replay attacks are modeled as two mutually independent Bernoulli distributed random variables. To depress the ratio of sampled data transmissions over the network, the dynamic version of event‐triggered transmission policy is properly proposed. Then, criteria of stochastically admissible for the filtering error systems guaranteeing mixed H∞$$ {H}_{\infty } $$ and passive performance are addressed via linear matrix inequalities (LMIs). The gains of resilient filter and the dynamic event‐based transmission policy can be simultaneously gained by optimizing the LMIs. Finally, two examples that include a numerical example and a direct current motor system are provided to testify the feasibility and effectiveness of the developed technique. [ABSTRACT FROM AUTHOR]

The purpose of this article is to propose a novel framework employing a looped‐functional approach for the stability analysis of continuous‐time linear systems with asynchronous sampling. In this approach, a negative forward‐difference of a Lyapunov functional consisting of a Lyapunov function and a looped‐functional sufficiently guarantees asymptotic stability of the sampled‐data systems. To reduce the conservatism of the stability criteria, we develop a consecutive time‐intervals‐dependent looped‐functional approach that satisfies a convex looping inequality with respect to each sampling interval. Compared to the existing looped‐functional approaches, the proposed method provides a more general looped‐functional and in turn a more relaxed stability conditions. The existing looped functionals and their associated looping conditions can be considered as special cases of the proposed ones. This relationship can easily be verified by excluding time‐intervals‐dependent terms in the general looped functional. Four numerical examples that consider both periodic and asynchronous sampling cases demonstrate that the proposed looped‐functional approach shows better performance in terms of allowable maximum sampling intervals at a cost of a small additional number of decision variables. [ABSTRACT FROM AUTHOR]

Rehabilitation exoskeleton robots play a crucial role in restoring functional lower limb movements for individuals with locomotor disorders. Numerous research studies have concentrated on adapting the control of these rehabilitation robotic systems. In this study, we investigate an affine state-feedback control law for robust position control of a knee exoskeleton robot, taking into account its nonlinear dynamic model that includes solid and viscous frictions. To ensure robust stabilization, we employ the Lyapunov approach and propose three methods to establish stability conditions using the Schur complement, the Young inequality, the matrix inversion lemma, and the S-procedure lemma. These conditions are formulated as Linear Matrix Inequalities (LMIs). Furthermore, we conduct a comprehensive comparison among these methods to determine the most efficient approach. At the end of this work, we present simulation results to validate the developed LMI conditions and demonstrate the effectiveness of the adopted control law in achieving robust position control of the knee exoskeleton robot. [ABSTRACT FROM AUTHOR]

The simultaneous fault detection and control (SFDC) has emerged as a reliable scheme. However, what happens when the designed structure undergoes changes? Such variations have the potential to cause instability and misdiagnosis. This paper delves into a cutting-edge SFDC structure that surpasses conventional designs in terms of reliability. The proposed Resilient Simultaneous Fault Detection and Control (RSFDC) structure considers variations in the designed parameters and provides a more robust and fault-tolerant approach to SFDC, with important implications for the design of reliable and resilient control systems in a broad range of applications. This scheme is formulated as a multi-objective optimisation problem, encompassing control and diagnosis objectives. Specifically, it aims to minimise the impact of faults and disturbances on the controlled output while reducing residual sensitivity to all changes and maximising the fault effects on the residual. Through simulation comparisons, this paper showcases the merits of the RSFDC structure in two examples, highlighting its superiority over other designs. [ABSTRACT FROM AUTHOR]