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The time-varying delay is a peculiar phenomenon that occurs in almost all systems. It can cause numerous problems and instability during system operation. In this paper, the time-varying delay is considered in both the states and input vectors, which is a significant distinction between the proposed method here and previous algorithms. Furthermore, the time-varying delay is unknown but bounded. To address this issue, the Razumikhin approach is applied to the proposed method, as it incorporates a Lyapunov function with the original non-augmented state space of the system models, in contrast to the Krasovskii formula. Moreover, the Razumikhin method performs better and avoids the inherent complexity of the Krasovskii method, particularly when dealing with large delays and disturbances. For achieving output stabilization, the model predictive control (MPC) is designed for the system. The considered system in this paper is an interval type-2 (IT2) fuzzy T-S model, which provides a more accurate estimation of the dynamic model of the system. The online optimization problems are solved using linear matrix inequalities (LMIs), which reduces the computational burden and online computational costs compared to offline and non-LMI approaches. Finally, an example is provided to illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The main focus of this article is to explore the finite‐time stabilization of time‐varying cyber‐physical systems (CPS) that are operating over multipath networks and under random denial‐of‐service (DoS) attacks. In contrast to prior studies, we present a set of necessary and sufficient conditions for achieving finite‐time stability in the closed‐loop model of CPS operating over single‐path network. Notably, this equivalent conditions are established based on the analysis of the state transition matrix (STM). Additionally, we utilized auxiliary systems to study more general CPS operating over multipath networks and obtained a sufficient condition based on STM. Finally, we address a sufficient condition based on the Lyapunov function and introduce a linear matrix inequality (LMI)‐based approach that facilitates the computation of nonfragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of multi‐objective robust fault estimation based on observer is addressed for T‐S fuzzy nonlinear singularly perturbed systems with time‐varying state delay and external disturbance. Under H∞$$ {H}_{\infty } $$ performance constraint, a fuzzy augmented fault estimation observer is introduced to improve the performance of actuator and sensor fault estimation simultaneously. The sufficient conditions for the existence of fault estimator are given in the form of LMIs, where ε$$ \varepsilon $$‐dependent Lyapunov function is considered. The given multi‐objective fault estimator design strategy has a good ability to suppress external disturbance and ensure the estimation accuracy and convergence rate work well for all ε∈(0,ε‾]$$ \varepsilon \in \left(0,\overline{\varepsilon}\right] $$. Then the largest stability bound and the best attenuation capacity are guaranteed by deriving a modified optimal algorithm. Finally, two examples are given to illustrate the feasibility and correctness of the proposed design method. [ABSTRACT FROM AUTHOR]

This paper investigates finite time annular domain (FTAD) stability and stabilisation for Itô-type stochastic time-varying systems with continuous Wiener and discontinuous Poisson noises (STVSWPNs). First, using Itô-Levy formula and time-varying multiple quadratic Lyapunov functions, two less conservative FTAD-stability conditions based generalised differential Lyapunov equations (GDLEs) and differential linear matrix inequalities (DLMIs) are obtained. Second, the FTAD stabilisation is studied and some new sufficient conditions for the existence of state feedback and static output feedback controllers are presented by tractable differential linear matrix inequalities. Moreover, a new numerical algorithm is given. Finally, a numerical example and a real-world example are utilised to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This work devotes to the security consensus problems for time-varying multi-agent systems (MASs) based on event-triggered control method with denial-of-service (DoS) attacks and parameter uncertainties. During information transmission, DoS attacks exist in both control and measurement channels, regarded as a dwell-time switching scheme, and hence the augmented system can be transformed into a class of discrete-time switched system subject to dwell-time property which contains an unstable and a stable subsystem. To increase the utilization of communication resources, the control input signal can be updated by adopting a novel event-driven mechanism with state-dependent threshold over a given finite horizon. By utilizing multiple Lyapunov functions analysis strategy, two sufficient conditions are obtained to achieve the desired H ∞ consensus performance. The cone complementary linearization algorithm is employed to cope with the nonlinear terms, and the desired controller gain matrices are calculated via resolving the corresponding linear matrix inequalities. Finally, the effectiveness of this proposed method is verified by providing a simulation example and the multi-automobile system. [ABSTRACT FROM AUTHOR]

This paper considers the problem of designing a shifting state-feedback controller via quadratic parameter-dependent Lyapunov functions (QPDLFs) for systems subject to symmetric time-varying saturations. By means of the linear parameter varying (LPV) framework and the use of the shifting paradigm and the ellipsoidal invariant theory, it is shown that the solution to this problem can be expressed with linear matrix inequalities (LMIs) which can efficiently be solved via available solvers. Specifically, three hyper-ellipsoidal regions are defined in the state-space domain for ensuring that the control action remains in the linearity region of the actuators where saturation does not occur. Furthermore, the closed-loop convergence speed is regulated online according to the instantaneous saturation limit values through the shifting paradigm concept. The main characteristics of the proposed approach are validated by means of two illustrative examples. • State-feedback controller design for systems subject to time-varying saturations. • The convergence speed of the closed-loop response is varied online. • Design via parameter-dependent Lyapunov functions and ellipsoidal invariant theory. • The design conditions are expressed as a set of linear matrix inequalities (LMIs). • Simulation results validate the effectiveness through two illustrative examples. [ABSTRACT FROM AUTHOR]

This study is concerned with the stability analysis and the feedback stabilization problems for a class of uncertain switched nonlinear systems with multiple time-varying delays. Unusually, more general time delays, which depend on the subsystem number, are considered. In this regard, by constructing a novel common Lyapunov function, using the aggregation techniques and the Borne and Gentina criterion, new algebraic stability and feedback stabilization conditions under arbitrary switching are derived. The proposed results are explicit and obtained without searching a common Lyapunov function through the linear matrix inequalities approach, considered a difficult matter in this case. At last, two numerical simulation examples are shown to prove the practical utility of the suggested approach. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to explore the finite-time stabilization of mean-field time-varying stochastic systems that are affected by uncertain parameters, multiple disturbances, and delays. In contrast to prior studies, we present a set of sufficient conditions for achieving finite-time stability in the closed-loop model. Notably, these conditions are established based on the analysis of the state transition matrix (STM). Additionally, we address a sufficient condition based on the Lyapunov function, where the STM significantly simplifies the selection process of the Lyapunov function. Finally, we introduce a linear matrix inequality (LMI)-based approach that facilitates the computation of non-fragile controllers. The effectiveness of the developed theoretical results is verified through a stock investment model. [ABSTRACT FROM AUTHOR]

In this paper, a novel unknown input observer (UIO) design for discrete-time linear parameter-varying (LPV) with inexact scheduling parameters is addressed. The proposed approach is particularly relevant as most LPV design conditions require that the time-varying parameters of the system are completely known and real-time available. Therefore, such strategies do not present adequate formulations to deal with such types of uncertainty. Moreover, UIOs have significant applications in different areas, such as fault detection and isolation problems. Existence conditions for the UIO are provided in order to properly handle the mismatch along with the presence of unknown inputs in the LPV system. The design conditions are based on an input-to-state stability approach obtained from a parameter-dependent Lyapunov function and are cast in the form of Linear Matrix Inequalities. The effectiveness of the proposed methods is illustrated using a numerical example. [ABSTRACT FROM AUTHOR]

The problem of input–output stability analysis and stabilisation of discrete Takagi–Sugeno (T–S) fuzzy systems with a time-varying delay via an input–output (I–O) approach is investigated in this paper. Using a three-term approximation-based model, a forward subsystem with three constant delays and a feedback subsystem are presented. Two separate input–output stability criteria have been formulated, using an input–output approach and a scaled small gain theorem: a criterion based on the lifting method, a non-quadratic Lyapunov function, and bounded real lemma, another criterion based on a non-quadratic Lyapunov–krasovskii functional approach. Using this result, the input–output stabilisation problem is resolved through the so-called parallel distributed compensation (PDC) scheme. The conditions obtained are presented in terms of linear matrix inequalities (LMIs). Three numerical examples are provided to demonstrate the advantages and merit of the proposed method. [ABSTRACT FROM AUTHOR]

This paper focuses on a new H2 state‐feedback control synthesis for discrete‐time polytopic linear parameter‐varying (LPV) systems. The synthesis conditions have been derived using an approach less conservative than those currently found in the literature, which allows to deal with polytopic LPV systems subject to time‐varying parameters in all matrices of its state‐space representation. Based on parameter‐dependent Lyapunov functions, a set of linear matrix inequalities‐based conditions is provided to obtain a discrete‐time H2 state‐feedback controller. Another significant advantage of the proposed conditions is the ability to include the poly‐quadratic condition as a particular case, presenting a solution to this so far unresolved problem. In addition, using the same concept, an improved condition for quadratic H2 control synthesis is given. Finally, the effectiveness of the proposed state‐feedback control design method is assessed and compared to that of similar approaches by means of numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we study uniform, uniform asymptotic, and input-to-state stability conditions for nonlinear time-varying systems. We introduce an easily verifiable condition for uniform attractivity by utilizing an indefinite sign upper bound for the derivative of the Lyapunov function. With this bounding structure, we propose novel conditions that enable us to test uniform stability, uniform asymptotic stability, and ISS, easily. As a result, the constraints on the coefficients of the bound that identify uniformity for stability and attractivity, and many of the available conditions have been relaxed. The results are also used for the perturbation problem of uniformly stable and uniformly asymptotically stable linear time-varying systems. Consequently, we demonstrate that uniform asymptotic stability of nonlinear time-varying systems can be robust for perturbations, but with special time-varying coefficients. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of non-fragile H ∞ control for periodic piecewise time-varying systems. Based on a Lyapunov function with continuous time-varying Lyapunov matrix polynomial, and combining with the positiveness and negativeness properties of matrix polynomials, the H ∞ performance analysis is first accomplished. Then consider two types of controller gain perturbations that are formulated by time-varying matrix parameters and norm-bounded uncertainties. The additive and multiplicative non-fragile controllers to guarantee the H ∞ performance of the system are formed, of which the controller gain could be solved with linear matrix inequalities directly. The designed non-fragile H ∞ controller is desirable in applications. Finally, numerical examples demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the problem of the event‐triggered H∞ control for network descriptor systems with time‐delay under a novel adaptive event‐triggering scheme. First, to save more limited communication resource, a novel adaptive event‐triggering scheme is introduced to adaptively adjust the communication threshold. Second, by considering the network‐induced delay, the system's time‐varying delay, and the transmission scheme, a delay system method is used to build a novel time‐varying delay system model. Based on this model and Lyapunov function technology, sufficient stability conditions with the H∞ disturbance performance to verdict admissible and stabilization conditions to codesign the controller gain are obtained in terms of linear matrix inequalities. Then, an event‐triggered H∞ controller is proposed to stabilize descriptor systems with time‐delay. Finally, a numerical simulation example and a comparing example are employed to illustrate the effectiveness and the advantageous performances of the proposed adaptive event‐triggering scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the pole assignment stabilization with memory state feedback controllers for switched nonlinear time-varying delay systems. More general time-varying delays which depend on the subsystem number are considered. Based on novel common Lyapunov functions (CLFs), the aggregation techniques, the proprieties and the Borne–Gentina criterion, new algebraic stabilization criteria are established. The proposed design can guarantee the stability of the closed-loop systems under arbitrary switching. It allows to avoid researching a common Lyapunov function (CLF), considered a difficult matter. Four illustrate examples were finally utilized to exhibit the effectiveness of the obtained results. • We address the stabilization problem with memory state feedback controllers through the pole assignment control. • Design for a class of both continuous and discrete-time switched nonlinear systems with time-varying delays under arbitrary switching. • Considered time-varying delays depend on the subsystem number. • The main technical difficulties for this problem lie in finding an appropriate common Lyapunov function for all subsystems. • Novel memory state feedback stabilization criteria through the pole assignment control are established with the help of new contracted common Lyapunov functions, using the aggregation techniques, the M - matrix approach and the Borne–Gentina criterion. • Proposed methods are algebraic, simple to use and obtained without any computations over linear matrix inequalities constraints and they can constitute interesting alternative to construct a common Lyapunov function considered as a hard task. [ABSTRACT FROM AUTHOR]

In this paper, stability and stabilisation of switched time-varying delay systems are investigated. By developing, a multiple discontinuous Lyapunov function approach and using the mode-dependent average dwell time (MDADT) switching signal, sufficient conditions are first proposed to guarantee the exponential stability of the switched system with stable and unstable subsystems where the time-varying delay is considered in the states. Relaxed stability conditions are also obtained by using a form of the Bessel–Legendre inequality. Then stabilisation of the proposed system is presented by designing a sliding mode controller. Sufficient conditions and sufficient relaxed conditions of a reduced-order sliding mode dynamics are derived, and desired sliding surfaces in the form of linear matrix inequalities (LMIs) are also given. The obtained conditions are checked by using the combined genetic algorithm and convex programming techniques. Moreover, some numerical and practical examples are given to illustrate the effectiveness of the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses a pole‐assignment control problem for discrete‐time linear parameter varying (LPV) systems. Based on LPV modeling approach, time‐varying systems can be mathematically described via combining several linear systems and a specific weighting function. For the LPV systems, gain‐scheduled (GS) control scheme is applied to deal with stabilization problem subject to pole‐assignment constraint. Moreover, two cases of Lyapunov function are respectively employed to derive some sufficient conditions which belong to linear matrix inequality (LMI) problems. Solving those derived conditions, the corresponding GS scheduled controller can be designed such that the asymptotical stability and pole assignment of LPV systems are guaranteed. Finally, a controller problem of truck‐trailer system is used to demonstrate the applicability and effectiveness of the proposed design methods. [ABSTRACT FROM AUTHOR]

In this paper, based on time-varying delay Markovian jump system (MJS), Bessel-Legendre inequality method and improved positive definite condition of Lyapunov function are used, and parallel distributed compensation (PDC) state feedback controller is also introduced. The conservatism of the system is reduced by using this inequality method and positive definite conditions, and further decreases with the increase of the Legendre parameter N. The PDC controller considers two control parameters simultaneously, which can represent the actual system more truthfully. Finally, Example 1 proves the effectiveness of the improved method in this paper. Example 2 considers time-varying probability transition perturbations. Example 3 obtains the parameters of PDC controller with different parameters N. Example 4 illustrates the practical significance of methods in this paper by introducing a time-delay inverted pendulum system with Markovian parameters. [ABSTRACT FROM AUTHOR]

The integration of renewable energy resources to DC microgrid has captured the attention of the researchers in recent years. One of the active field of application of DC distribution is the islanded DC microgrid (DC ImG). The DC ImG present numerous challenges to researchers. Among many challenges, the regulation of voltage and stability of the system is indispensable to efficient operation. The voltage stability problem becomes more prominent when the system is exposed to disturbances and possess uncertainties in parameters. However, challenges can be overcome by skilful design of a robust controller for the system. Therefore, in this paper, an output-feedback based centralized robust control scheme is proposed. The proposed controller is designed to maintain good control performance in the presence of parametric uncertainties and exogenous disturbances. The uncertainties of the DC microgrid is modelled as a linear time-varying state-space system. The upper and the lower bounds of the time-varying parameters are determined by a Lebesque-measurable matrix. To attenuate the exogenous disturbances of the system H ∞ based output-feedback controller is designed. The system stability is assured by the Lyapunov function candidate. The output-feedback controller needs only the voltage measurement; therefore, it requires less communication bandwidth as compared to the state-feedback. To obtain the controller parameters linear matrix inequality constraints are formulated and solved. The performance of the proposed controller is verified via simulations and compared with the existing schemes. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of full-order and reduced-order fault detection filter (FDF) design under unified linear matrix inequality (LMI) conditions for a class of continuous-time singular Markovian jump systems (CTSMJSs) with time-varying delays and polytopic uncertain transition rates. By constructing a new Lyapunov function, sufficient conditions are firstly provided for the singular model error augmented system such that the system is stochastically admissible with an H ∞ performance level γ. And then, by applying a novel convex polyhedron technique to decoupled linear matrix inequalities, the full-order and reduced-order fault detection filter parameters can be obtained within a convex optimization frame. The reduced-order fault detection filter (FDF) can not only meet the fault detection accuracy requirements of complex systems but also improve the fault detection efficiency. Finally, a DC motor and an illustrative simulation example are given to verify the feasibility and effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

State estimation for switched systems with time-varying parameters has received a great attention during the past decades. In this paper, a new approach to design an interval observer for this class of systems is proposed. The scheduling vector is described by a convex combination so that the varying parameters belong into polytopes. The considered system is also subject to measurement noise and state disturbances which are supposed to be unknown but bounded. The proposed method guarantees both cooperativity and Input to State Stability (ISS) of the upper and lower observation errors. Sufficient conditions are given in terms of Linear Matrix Inequalities (LMIs) using a common quadratic Lyapunov function. Finally, a numerical example is provided to show the effectiveness of the designed observer. [ABSTRACT FROM AUTHOR]

This paper is concerned with the stability analysis of discrete-time systems with a time-varying delay. Different from the recent related works that reduce the conservatism by increasing the complexity of Lyapunov functions, this paper aims at conservatism-reduction by using relatively simple Lyapunov functions with an augmented double summation term. The key point for achieving this task is that a delay-dependent matrix-separation-based inequality is established to estimate the augmented-type summation term arising in the forward difference of Lyapunov functions. The proposed method provides a general form of inequalities, which realizes the effective reduction of estimation gap, and also introduces several tractable delay-dependent matrices, which achieves the full use of available delay-related information. As a result, for two types of time-varying delays, the usage of the proposed inequality under different separations leads to two less conservative and low complex stability criteria, whose advantages are demonstrated via three examples. [ABSTRACT FROM AUTHOR]

All real-world systems are affected by the saturation phenomenon due to inherent physical limitations of actuators. These limitations should be taken into account in the controller's design to prevent a possibly severe deterioration of the system's performance, and may even lead to instability of the closed-loop system. Contrarily to most of the control strategies, which assume that the saturation limits are constant in time, this paper considers the problem of designing a state-feedback controller for a system affected by time-varying saturation limits with the objective to improve the performance. In order to tie variations of the saturation function to changes in the performance of the closed-loop system, the shifting paradigm is used, that is, some parameters scheduled by the time-varying saturations are introduced to schedule the performance criterion, which is considered to be the instantaneous guaranteed decay rate. The design conditions are obtained within the framework of linear parameter varying (LPV) systems using quadratic Lyapunov functions with constant Lyapunov matrices and they consist in a linear matrix inequality (LMI)-based feasibility problem, which can be solved efficiently using available solvers. Simulation results obtained using an illustrative example demonstrate the validity and the main characteristics of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we address the robust H ∞ stabilization for T-S fuzzy systems with time-varying delays based on memory sampled-data control. By developing some new terms, an improved piecewise Lyapunov–Krasovskii functional (LKF) is constructed to take full advantage of characteristic about real sampling pattern. Furthermore, some relaxed matrices proposed in the LKF are not necessarily positive definite. By using the LKF and Free-Matrix-Based (FMB) integral inequality, some sufficient criteria are established to ensure the stability of fuzzy systems and reduce the influence of external disturbance with an H ∞ norm bound. Then, the memory sampled-data controller can be derived by solving a group of linear matrix inequalities (LMIs) with the maximal sampling period. Finally, a numerical example is given to demonstrate the benefits and the superiority of the approach proposed. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problems of stability and stabilization are considered for a class of switched linear systems with slow switching and fast switching. A multiple convex Lyapunov function and a multiple discontinuous convex Lyapunov function are first introduced, under which the extended stability and stabilization results are derived with a mode‐dependent average dwell time switching strategy, where slow switching and fast switching are exerted on stable and unstable subsystems, respectively. These two types of Lyapunov functions are established in a constructive manner by virtue of a set of time‐varying functions. By using our proposed approaches, larger stability regions of system parameters are identified, and tighter bounds can be obtained for the mode‐dependent average dwell time. New mode‐dependent and time‐varying controllers are constructed for a class of switched control systems with stabilizable and unstabilizable subsystems as well. All the stability and stabilization conditions can be given in terms of strict linear matrix inequalities (LMIs), which can be checked easily by using recently developed algorithms in solving LMIs. Finally, two numerical examples are provided to show the effectiveness of the obtained results compared with the existing results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, stochastic stability of neutral type Markovian-jumping bidirectional associative memory (BAM) neural networks is investigated. The jumping parameters are modeled as a continuous-time discrete-state Markov chain. The activation functions are supposed to be bounded and globally Lipschitz continuous. Furthermore, based on the Lyapunov–Krasovskii functional, a linear matrix inequality (LMI) approach is developed to establish sufficient conditions and novel delay-dependent conditions are established for the stochastic asymptotic stability of Markovian jumping BAM neural networks. The condition is presented in terms of linear matrix inequalities (LMIs), which can be easily checked by using MATLAB LMI toolbox. Finally, numerical examples are provided to show the effectiveness of the main results. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the problem of state estimation for a class of neural networks with discrete and distributed interval time‐varying delays. We propose a new approach of nonlinear estimator design for the class of neutral‐type neural networks. By constructing a newly augmented Lyapunov‐Krasovskii functional, we establish sufficient conditions to guarantee the estimation error dynamics to be globally exponentially stable. The obtained results are formulated in terms of linear matrix inequalities (LMIs), which can be easily verified by the MATLAB LMI control toolbox. Then, the desired estimators gain matrix is characterized in terms of the solution to these LMIs. Three numerical examples are given to show the effectiveness of the proposed design method. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a novel control scheme for systems with input and output time-varying delays is provided in discrete-time domain. The control strategy combines predictor-like techniques with a delay-dependent gain-scheduled extended state observer. The main goal is twofold: (i) to minimize the negative effect of time-varying delays in the closed-loop performance and, (ii) to actively compensate the effect of mismatched disturbances in the controlled output. Moreover, a sufficient condition based on Linear Matrix Inequalities (LMI) is provided to obtain the maximum delay interval that ensures the stability of the closed-loop system. Finally, the achieved benefits of the proposal are shown by simulation in open-loop unstable plants, and experimentally validated in a test-bed quadrotor platform. Highlights • A novel predictor-based control with extended state observer (ESO) is given. • Time-varying delays are considered both in input and output channels. • A delay-dependent gain scheduling strategy is integrated with the ESO. • The disturbance rejection and performance are improved compared with other similar approaches. • The effectiveness of the proposed method is validated through simulation and experimental setup. [ABSTRACT FROM AUTHOR]

Abstract It is well known that how to deal with the effect of time delay and how to determine the control and rest widths are the main difficulties for intermittent control. This paper considers asymptotic synchronization of drive-response memristive neural networks (MNNs) with bounded time-varying discrete delay and unbounded distributed delay (mixed delays), which extends existing intermittent control techniques and reveals new relationship between control width and rest width. A quantized intermittent control (QIC) is designed to save both channel resources and control cost and reduce both the amount of transmitted information and channel blocking. Based on weighted double-integral inequalities, novel Lyapunov–Krasovskii functionals with negative terms are designed, which reduce the conservativeness of obtained results greatly. Sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained to ensure the asymptotic synchronization. The control gains can also be designed by solving the LMIs. It is shown that the QIC can be neither periodic nor proportional between control width and rest width. Moreover, the relationships between control width, rest width, and convergence rate are explicitly given. Finally, numerical simulations are provided to illustrate the effectiveness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, the problem of nonfragile stabilization for uncertain systems with interval time‐varying delays via new double integral inequality approach is studied. Based on the auxiliary function‐based integral inequality, a new double integral inequality is developed in this literature. Then, to prove the potency of the proposed inequality, some less conservative stability conditions are derived with the help of Lyapunov‐Krasovskii functional and linear matrix inequality technique. Three benchmark illustrative examples are delivered with simulations to validate the effectiveness and advantages of present results. [ABSTRACT FROM AUTHOR]

The finite-time stabilisation, finite-time H∞ control and finite-time adaptive H∞ control problems for a class of nonlinear descriptor systems are studied. First, under a sufficient condition for the system impulse controllable, a finite-time stabilised controller is designed by a suitable state feedback. Then, the finite-time H∞ control and finite-time adaptive H∞ control problems are considered for the nonlinear descriptor system with external disturbances and/or parametric perturbations, respectively. Compared with the existing results, there is no constraint for singular matrix E, therefore controllers can be designed for more nonlinear descriptor systems. Finally, an example of the nonlinear descriptor circuit system with simulations is applied to illustrate the effectiveness of the finite-time controllers obtained in this study. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the observer‐based H∞ control of Markovian jump systems with interval time‐varying delays and incomplete transition rates. To reduce the conservatism of proposed results, a modified Lyapunov‐Krasovskii functional is constructed, where an improved delay partitioning method is used by partitioning the delay interval into multiple segments with a geometric sequence. Moreover, the Jensen‐based integral inequality and the reciprocally convex technique are used to tackle the time‐varying delays. Some less conservative stochastic stability criteria are derived in the framework of linear matrix inequalities. Then, the observer‐based H∞ controller is designed. Finally, three numerical examples are given to demonstrate the merit and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the problem of exponential stabilization for a class of switched nonlinear uncertain systems with time-varying delay is investigated based on a type of Lyapunov- Krasovskii functional, the free-weighting matrix technique and the average dwell time approach. Some exponential stability criteria are established in terms of linear matrix inequalities (LMIs) for switched nonlinear uncertain systems with delay. In addition, the feedback controller design algorithm for the system is given through the matrix deformation technique and Schur complement. Finally, a numerical example and a practical example of river pollution control are provided to show the validity and potential of the developed results. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with the problem of exponential H ∞ filtering for singular Markovian jump systems with time‐varying delays subject to sensor failures. The main objective is to design a reliable filtering such that the considered filtering error system in the presence of a time‐varying delay and sensor failures is mean‐square exponentially admissible with a specified decay rate and simultaneously satisfies an H ∞ performance. First, the delay interval is partitioned into m subintervals and a novel mode‐dependent stochastic Lyapunov‐Krasovskii functional is constructed. By using the reciprocally convex inequality in each subinterval, sufficient conditions of exponential H ∞ performance analysis are developed for the considered filtering error system. Then, based on these conditions, the existence conditions of the desired reliable filter are derived and the filter parameters are obtained. It should be mentioned that all the results presented here are not only dependent on the time delay but also dependent on the decay rate and the partitioning size. Furthermore, all the conditions are established in terms of strict linear matrix inequalities. Finally, two numerical examples are given to illustrate the less conservatism and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper concerns with the H∞ robust exponential stability and memory state feedback stabilization of singular Markov jump systems with time-delay and input saturation. Linear matrix inequality conditions are given to guarantee regularity, impulse-freeness and exponential stability for the singular Markov jump system. Moreover, sufficient conditions are presented to ensure the H∞ disturbance attenuation level, and the design method of memory feedback controller is developed by solving linear matrix inequalities optimization problem without any decompositions of system matrices and equivalent transformation. Furthermore, the function in the proof procedure belongs to multiple Lyapunov-like functions whose advantage lies in their flexibility. Finally, numerical examples are employed to verify the effectiveness of the proposed methods and to illustrate the significant improvement on the conservativeness of some reported results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, the globally asymptotical stability in the mean square for a class of high-order bidirectional associative memory neural networks with time-varying delays and fixed moments of impulsive effect are studied. The proof makes use of Lyapunov-Krasovskii functionals, and the conditions are expressed in terms of linear matrix inequalities. A controller has been derived to robustly stabilize this network. Two illustrative examples are also given at the end of this paper to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of dissipative filtering for a class of nonlinear singular Markovian Jump systems (SMJSs) with time-varying delays. Our consideration is centered on the design of a mixed filter that can contain both mode-dependent and mode-independent filters in a unified framework. By using a delay-decomposition approach and constructing a mode-dependent stochastic Lyapunov–Krasovskii functional, sufficient delay-dependent conditions are derived in terms of linear matrix inequalities, which guarantee the considered nonlinear SMJSs to be stochastically admissible with a dissipativity performance γ . Based on the conditions, the existence conditions and parameters of the desired filter are obtained. Two numerical examples are given to illustrate the reduced conservatism and the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of finding outer bound of forwards reachable sets and interbound of backwards reachable sets of generalized neural network systems with interval nondifferentiable time-varying delay and bounded disturbances. Based on constructing a suitable Lyapunov-Krasovskii functional and utilizing some improved Jensen integral-based inequalities, two sufficient conditions are derived for the existence of: (1) the smallest possible outer bound of forwards reachable sets and (2) the largest possible interbound of backwards reachable sets. These conditions are delay dependent and in the form of matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Three numerical examples with simulation results are provided to demonstrate the effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, sampled-data H filtering problem is considered for Markovian jump singularly perturbed systems with time-varying delay and missing measurements. The sampled-data system is represented by a time-delay system, and the missing measurement phenomenon is described by an independent Bernoulli random process. By constructing an ε-dependent stochastic Lyapunov– Krasovskii functional, delay-dependent sufficient conditions are derived such that the filter error system satisfies the prescribed H performance for all possible missing measurements. Then, an H filter design method is proposed in terms of linear matrix inequalities. Finally, numerical examples are given to illustrate the feasibility and advantages of the obtained results. [ABSTRACT FROM AUTHOR]

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The H∞ robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal H2/H∞ bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The H2/H∞ observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics. [ABSTRACT FROM AUTHOR]

This paper considers the finite-time stability and finite-time boundedness problems for switched neural networks subject to L2-gain disturbances. Sufficient conditions for the switched neural networks to be finite-time stable and finite-time bounded are derived. These conditions are delay-dependent and are given in terms of linear matrix inequalities. Average dwell time of switching signals is also given such that switched neural networks are finite-time stable or finite-time bounded. By resorting to the average dwell time approach and Lyapunov–Krasovskii functional technology, some new delay-dependent criteria guaranteeing finite-time boundedness and stabilizability with L2-gain analysis performance are developed. An illustrative example is given to demonstrate the effectiveness of the proposed state estimator. [ABSTRACT FROM AUTHOR]

In this paper, we put in effort to inspect the passivity and exponential passivity problem of memristive neural networks with time-varying delays and reaction–diffusion term. Based on the basis of generalized Lyapunov approach, Poincar e ` inequality, Schur complement Lemma, free-weighting matrix approach as well as some inequality techniques, the main conclusions of this paper are derived in the form of linear matrix inequality (LMI). What is noteworthy is that the obtained sufficient criteria rely on the reaction–diffusion term, which implies that the reaction–diffusion term can effect the passivity of the given system. Finally, two numerical examples are emerged to check the practicability of the derived passivity conditions. [ABSTRACT FROM AUTHOR]

In this paper we investigated the problem of the finite-time stability for a class of memristor based switched neural networks with time-varying delays. By constructing proper Lyapunov functionals. Based on the average dwell time technique, mode-dependent average dwell time technique and using a free-matrix-based integral inequality, Jensen’s inequality are used to estimate the upper bound of the derivative of the LKF, several sufficient conditions are given to ensure the finite-time stability of the memristor-based switched neural networks with discrete and distributed delays in the sense of feasible solutions. The finite-time stability conditions here are presented in terms of linear matrix inequalities, which can be easily solved by using Matlab Tools. Finally, the numerical examples are provided to verify the effectiveness and benefit of the proposed criterion. [ABSTRACT FROM AUTHOR]

In this study, the authors investigate the problem of finite-time output regulation for a class of mismatched uncertain n-dimensional integrator, in which only the output signal is measurable and the higher derivatives of the matched and mismatched disturbances are bounded by time-varying functions. Based on a finite-time extended state observer, an output feedback controller is constructed. It is shown that even in the presence of mismatched uncertainties, whose high-order derivatives are bounded by positive functions, the output of the system can be regulated to zero in finite time without requiring the knowledge of full-state signals. An application to mass-spring mechanical systems is given to illustrate the effectiveness and attractive properties of the authors' proposed controller. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of stability analysis for generalized delayed neural networks with interval time-varying delays based on the delay-partitioning approach. By constructing a suitable Lyapunov-Krasovskii functional with triple- and four-integral terms and using Jensen's inequality, Wirtinger-based single- and double-integral inequality technique and linear matrix inequalities (LMIs), which guarantees asymptotic stability of addressed neural networks. This LMI can be easily solved via convex optimization algorithm. The novelty of this paper is that the consideration of a new integral inequalities and Lyapunov-Krasovskii functional is shown to be less conservatism, and it takes fully the relationship between the terms in the Leibniz-Newton formula within the framework of LMIs. Moreover, it is assumed that the lower bound of the time-varying delay is not restricted to be zero. Finally, several interesting numerical examples are given to demonstrate the effectiveness and less conservativeness of our theoretical results over well-known examples existing in recent literature. [ABSTRACT FROM AUTHOR]