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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 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]

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]

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]

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]