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This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods. [ABSTRACT FROM AUTHOR]

This paper is concerned with asynchronous finite-time H ∞ control for a class of discrete-time switched linear systems via admissible edge-dependent average dwell time (AED-ADT) approach. Firstly, by considering the switching time delay between the system and the state feedback controller, appropriate Lyapunov functions are constructed for asynchronous and synchronous switching, respectively. Secondly, for the existence of a set of state feedback controllers, a sufficient condition which guarantees the finite-time boundedness of the closed-loop system with AED-ADT is proposed. Thirdly, a sufficient condition for finite-time H ∞ control with a prescribed H ∞ performance is further developed based on the obtained result. Finally, a numerical example is given to verify the validity of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

We study the stability of discrete-time switched systems for any laws of switching between linear subsystems. Pairwise connected systems are distinguished among such systems. A sufficient frequency-domain stability condition has been obtained for them. Two sufficient conditions and two criteria for the existence of a Lyapunov quadratic function are obtained for switched systems whose stability is equivalent to the absolute stability of Lur'e systems with two nonlinearities. These conditions amount to checking the solvability of special matrix inequalities whose dimensions are considerably lower than the dimension of the original system of matrix inequalities that defines the necessary and sufficient conditions. The resulting conditions are compared with the conditions of the Tsypkin criterion and with the necessary and sufficient conditions using the examples of systems of the third and sixth orders. [ABSTRACT FROM AUTHOR]

The finite-time event-triggered H ∞ filtering of the discrete-time switched linear systems with time delay is addressed in the paper. The switched system and its filtering switched system are established as a filtering error system (FES) with augmented switching signal by the merging switching signal technique. The asynchronous switching phenomenon of switched system modes and filter modes occurs since a mode-dependent event-triggered transmission scheme (METS) which determines the system output and switching signal is addressed. Meanwhile, by the average dwell time (ADT) and multi-Lyapunov functional method, some sufficient conditions are given to make certain that the FES is finite-time bounded (FTB) and has a specified H ∞ performance. Furthermore, the finite-time H ∞ filter is designed by solving linear matrix inequalities. Ultimately, a numerical example is inspired to manifest the availability of the effects in the study. [ABSTRACT FROM AUTHOR]

This article addresses the input‐to‐state stability (ISS) problem for general discrete‐time impulsive and switched delayed systems coupled by delay‐dependent impulses. In our studied systems, the impulsive signal has a large degree of freedom, that is, the impulse effect can occur simultaneously with or different from the switching effect. A new Lyapunov–Krasovskii functional is proposed to deal with the delay effect of switching signal and impulsive jump, which is divided into the delay‐independent part and delay‐dependent part. A new concept named admissible edge‐dependent average impulsive interval (AED‐AII) is set up to characterize the impulse sequence relative to the admissible edge‐dependent average dwell time (AED‐ADT) concept of the switching signal. Based on AED‐ADT approach and AED‐AII technique, some improved sufficient outcomes guaranteeing ISS of discrete‐time impulsive and switched delayed systems are presented, respectively, for stabilizing and destabilizing delay‐dependent impulses. Meanwhile, the relationship among AED‐AII, AED‐ADT, the jump amplitude of switching signal and impulse signal at their respective discrete points, the decay rate of Lyapunov functional for system dynamics is connected to pursue ISS of the whole system. Compared with previous works, our setups enjoy the following characteristics: it thoroughly digs the influence of time delay existing in impulses and system dynamics on the function part of L‐K functional, which are less conservative relative to other works; the proposed AED‐ADT switching signals and AED‐AII jump signals cover a large set of hybrid systems. Two numerical examples are given to illustrate the effectiveness and less conservativeness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered H ∞ filtering problem for discrete-time linear switched systems is investigated under asynchronous switching. Under the mode-dependent event-triggered transmission mechanism (METM), the switching signal and filtering signal are combined into an augmented switching signal by merging signal technology, and the switched system and filtering system are modeled as a filtering error system (FES). Because the switching signal of the filtering system is determined by METM, there will be an asynchronous switching phenomenon between the switched system and filtering system. The novel sufficient conditions are given to ensure that the FES is finite-time bounded (FTB) and has a specified H ∞ performance by the average dwell time (ADT) and multi-Lyapunov functional method. And based on this, the design method of the H ∞ filter is given. Ultimately, the numerical examples are inspired to manifest the availability of the effects in the study. [ABSTRACT FROM AUTHOR]

In this paper, the finite-frequency fault detection filter design for discrete-time switched systems is investigated. The frequencies of the faults and the unknown disturbance input are assumed to be finite and in three known intervals, qualified as low-, middle-, and high-frequency intervals. Based on the switched Lyapunov function and the generalized Kalman-Yakubovic-Popov lemma, efficient conditions are obtained to guarantee the existence of a finite-frequency fault detection filter, such that the error system is asymptotically stable with an H∞/H- performance index. Finally, a chemical reactor control system is employed to illustrate the obtained techniques.

In this paper, the problem of l2-l∞ control is investigated for the sampled-data systems including packet dropout. The sampled-data system is modeled as a discrete-time switched system based on the number of lost packets. Then the controller is designed to guarantee the discrete-time switched system is exponentially stable with a prescribed l2-l∞ performance subject to mode dependent average dwell time approach. The sufficient conditions to solve the controller gain is derived via a set of linear matrix inequalities (LMIs). Finally, an example is presented to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

This paper considers the problems of the robust stability analysis and H∞ controller synthesis for uncertain discrete‐time switched systems with interval time‐varying delay and nonlinear disturbances. Based on the system transformation and by introducing a switched Lyapunov‐Krasovskii functional, the novel sufficient conditions, which guarantee that the uncertain discrete‐time switched system is robust asymptotically stable are obtained in terms of linear matrix inequalities. Then, the robust H∞ control synthesis via switched state feedback is studied for a class of discrete‐time switched systems with uncertainties and nonlinear disturbances. We designed a switched state feedback controller to stabilize asymptotically discrete‐time switched systems with interval time‐varying delay and H∞ disturbance attenuation level based on matrix inequality conditions. Examples are provided to illustrate the advantage and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the H ∞ control is investigated for a class of discrete-time switched systems. The switching delay between the mode and controller, which leads to the asynchronism, is taken into consideration. The switching signal is considered to be constrained by persistent dwell time (PDT), which is known to be more general than the common used dwell time or average dwell time. Sufficient conditions to guarantee the asymptotic stability and ℓ 2 -gain are derived under a PDT scheme. By considering that actual controllers are subjected to norm-bounded gain perturbations, non-fragile controllers are designed based on both state feedback and output feedback stategies. Finally, the effectiveness of the provided methods is illustrated by two examples. [ABSTRACT FROM AUTHOR]

The event-triggered control problem for discrete-time switched linear systems with packet losses is addressed in this paper. It is assumed that, at each event-triggered instant transmitted successfully, the controller can only access the transmitted information of system state and mode. In both cases of packet losses and no packet losses, mode dependent event-triggered transmission schemes are proposed. And the closed-loop system is modeled as a switched system with augmented switching signal. Then, based on the multiple Lyapunov function method, in the case of packet losses, exponential stability conditions are given with constraint of the maximum allowable number of successive packet losses, and design methods for state feedback controller gains and mode dependent event-triggered parameters are obtained. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the event-triggered H ∞ filtering problem for discrete-time switched linear systems is addressed. The filter and the system are connected via a communication network, and the transmitted information of system output and switching signal is determined by an event-triggered transmission scheme, which contains system mode dependent parameters. Consequently, the asynchronous switching between the filter and the system occurs, and the filtering error system is modeled as a switched system with augmented switching signal by using the merging switching signal technique. Then, by the multiple Lyapunov function method, a new sufficient condition is obtained such that the filtering error system is exponentially asymptotically stable and satisfies the weighted H ∞ performance. Finally, the design method for the filter and event-triggered parameters is proposed by solving a set of linear matrix inequalities. Numerical simulations illustrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of reachable set estimation and synthesis for a class of discrete-time switched linear systemswith time delay and bounded peak disturbance. Combined with the feature of mode-dependent average dwell time switching, a new algorithm is developed to estimate the reachable set of switched system, which is both quasi-time-dependent and mode-dependent. Then, the proposed method is applied to time-delay system and a sufficient condition is presented to guarantee the asymptotic stability and estimate the bounding ellipsoid. Furthermore, the quasi-time-dependent controller is designed to stabilize the system and restrict the closed-loop system states to an ellipsoidal bound. Examples are presented to illustrate the effectiveness and advantages of the obtained theorems. [ABSTRACT FROM AUTHOR]

The problem of stability is studied in this paper for a class of discrete-time switched systems with unstable subsystems. Two new definitions of slow switching and fast switching on the basis of admissible edge-dependent average dwell time are proposed, respectively. Some conditions are established by using multiple Lyapunov function method to guarantee the global uniform exponential stability of discrete-time switched systems. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

The problems of stability and l 2 − l ∞ filtering are studied in this paper for a class of discrete-time switched systems. A novel admissible edge-dependent average dwell time switching is proposed on the basis of the directed graph. A condition ensuring the global uniform exponential stability of discrete-time switched systems is established. A new inequality that depicted the relation between Lyapunov-like function and disturbances is presented to guarantee the l 2 − l ∞ performance. Combined with the multiple Lyapunov-like function technology, the filtering error system is proved to be globally uniformly exponentially stable with l 2 − l ∞ performance, and the corresponding filter can also be obtained. Finally, three numerical examples are illustrated to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of actuator fault estimation observer design for discrete-time switched systems with finite-frequency. The frequencies of the fault and the unknown input disturbance are assumed to be in a finite range. A finite frequency fault estimation observer is proposed to estimate the actuator fault in the entire frequency domain. Based on the generalized Kalman–Yakubovic–Popov (KYP) lemma and the switched Lyapunov function method, the efficient conditions are obtained to achieve the fault estimation observer design. Finally, an example is given to illustrate the proposed technique. [ABSTRACT FROM AUTHOR]

This paper investigates the problems of actuator fault estimation and accommodation for discrete-time switched systems with state delay. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault and state delay. Then based on the obtained online fault estimation information, a switched dynamic output feedback controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This paper studies the mean-square stability of discrete-time linear switched systems with random switching, where the switching signal is the output of a logic dynamical switching model driven by an independent and identically distributed (i.i.d.) process. This class of switching is referred to as the modeled random switching. By regarding the switching model as a part of the system, a combined switched system with i.i.d. switching is obtained, which is of a hybrid nature, that is, the augmented state vector has both logic and continuous components. The semi-tensor product of matrices and the vector representation of logic are applied to merge the logic and the continuous components of the state. The equivalence between the mean-square stability of the original switched system and that of the merged switched system under i.i.d. switching is proved. By deriving the dynamics of the column-stacking form of the covariance matrix, necessary and sufficient conditions of mean-square stability for discrete-time linear switched systems with modeled random switching are obtained. An illustrative example is provided to demonstrate the usage of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of dynamic output feedback fault tolerant controller design for discrete-time switched systems with actuator fault. By using reduced-order observer method and switched Lyapunov function technique, a fault estimation algorithm is achieved for the discrete-time switched system with actuator fault. Then based on the obtained online fault estimation information, a switched dynamic output feedback fault tolerant controller is employed to compensate for the effect of faults by stabilizing the closed-loop systems. Finally, an example is proposed to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

This study is concerned with the generalised ℋ2 fault detection problem for a class of discrete‐time switched systems with repeated scalar non‐linearities. To reduce the overdesign of the quadratic framework, this study proposes a switching‐sequence‐dependent Lyapunov function approach to the fault detection filter design procedure. Sufficient conditions are obtained for the existence of admissible generalised ℋ2 fault detection filter. Since these conditions involve matrix equalities, the cone complementarity linearisation procedure is employed to cast the non‐convex feasibility problem into a sequential minimisation problem subject to linear matrix inequalities, which can be readily solved by using the standard numerical software. If these conditions are feasible, a desired fault detection filter can be easily constructed. Finally, a numerical example is given to illustrate the effectiveness of the proposed theory. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the robust H ∞ filter scheme for the discrete-time switched systems with interval time-varying delay and linear fractional perturbations is proposed. A convex optimization problem with some LMI constraints is formulated to design the stable switched filter which minimizes the H ∞ norm bound for filtering error system. Some nonnegative inequalities and the free weighting matrix technique are used to provide the additional degree of freedom which improves the conservativeness of the proposed results. Finally, a numerical example is illustrated to show the use of the main results. [Copyright &y& Elsevier]

The problem of observer-based finite-time exponential l2 − l∞ control is studied in this paper for a class of discrete-time switched systems with time delay and uncertainties. The observer-based controller is designed to guarantee that the developed closed-loop system is robust finite-time exponential l2 − l∞ stabilizable for all admissible uncertainties. 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 exponential l2 − l∞ performance are developed. The observer-based finite-time exponential l2 − l∞ controller is also designed by virtue of a cone complement linearization method. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper considers the design of robust H∞ filtering problem for switched stochastic discrete time-delay system with missing measurements via switched Lyapunov function approach. Attention is focused on the design of an exponentially stable filter guaranteeing a prescribed noise attenuation level in the H∞ sense and missing measurements probability. By using switched Lyapunov functionals, some sufficient conditions in terms of linear matrix inequalities (LMIs) are obtained. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the stabilization and robust H-infinity control of discrete switched system with time delay. The switching is time-driven and the design is based on the average dwell time method. The controller parameters and the permissible switching sequence, subject to the given average dwell time, can be obtained by solving a set of linear matrix inequalities (LMIs). Two examples are given to demonstrate the proposed methods. [Copyright &y& Elsevier]

Abstract: In this paper, the problem of delay-dependent filtering for a class of discrete-time switched systems with state delays is investigated under arbitrary switching using a parametrized approach. Attention is focused on the design of asymptotically stable filter guaranteeing a prescribed noise attenuation level in the sense. By using switched Lyapunov functionals, sufficient conditions for the solvability of this problem are obtained in terms of linear matrix inequalities (LMIs), the solution of which constructs the desired filter under arbitrary switching. Numerical examples are provided to demonstrate the effectiveness of the proposed techniques. [Copyright &y& Elsevier]

Abstract: In this paper, we investigate the problem of stabilization for single-input planar discrete-time switched systems by establishing necessary and/or sufficient conditions for the existence of switched quadratic Lyapunov functions of the closed-loop system. The results given in terms of a series of matrix inequalities generalize those results in our recent paper [Y.G. Sun, L. Wang, G. Xie, Necessary and sufficient conditions for stabilization of discrete-time planar switched systems, Nonlinear Anal.: Theory and Methods 65 (2006) 1039–1049] and clearly describe the set of switched quadratic Lyapunov functions for the system. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problems of robust stability, robust stabilization and H ∞ control via memoryless state feedback for uncertain discrete-time switched systems with mode-dependent time delays. Based on linear matrix inequalities (LMIs), a descriptor model transformation of the system and a switched Lyapunov function, new delay-dependent criteria are established which are not contained in known literatures. Numerical examples are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

Abstract: This paper investigates the generalized control problem for a class of discrete-time switched systems with uncertainties. The uncertain system is modelled as a polytopic type with linear fractional uncertainty in the vertices. By using switched Lyapunov functions, new linear matrix inequalities (LMIs) characterizing the generalized performance for discrete-time switched systems are obtained. Based on the result, a generalized output feedback controller is developed for uncertain discrete-time switched systems. A numerical example is included to demonstrate the effectiveness of the proposed result. [Copyright &y& Elsevier]

Abstract: In this paper, we consider the problems of robust stability and stabilization via memoryless state feedback for uncertain discrete-time switched systems with mode-dependent time-varying delays. By using a descriptor system method and linear matrix inequality technique, and by introducing a switched Lyapunov functional, we establish some new delay-dependent stability and stabilization criteria for the system. Numerical examples are presented to illustrate the effectiveness of the theoretical results. [Copyright &y& Elsevier]

The event-triggered control problem for discrete-time switched linear systems with network transmission delays is investigated in this paper. It is assumed that the controller can only access the transmitted information of system state and mode at each event-triggered instant. A mode dependent event-triggered transmission scheme is proposed and the closed-loop system is modeled as a switched system with delayed state and augmented switching signal. Then based on the multiple Lyapunov functional method, an exponential stability condition and design method for state feedback controller gains are obtained. The proposed approach leads an important step to study the event-triggered control for discrete-time switched systems. Finally, the effectiveness and improvement of the proposed approach are illustrated by a numerical example. [ABSTRACT FROM AUTHOR]