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This article explores the dissipative control of two‐dimensional (2‐D) discrete‐time switched Fornasini–Marchesini local state‐space systems under dwell‐time switching. It introduces a new point‐dependent convex storage function to establish the criteria for the asymptotic stability and strict (Q,S,R)$$ \left(Q,S,R\right) $$‐β$$ \beta $$‐dissipativity of the 2‐D switched Fornasini–Marchesini local state‐space model based on LMIs. From these established findings, special cases of dissipative control such as strict passivity and H∞$$ {H}_{\infty } $$ performance can be derived. The article also presents the design of a state feedback point‐dependent convex controller using the proposed storage function approach, along with a sufficient condition for the dissipativity of the closed‐loop system. Finally, several examples are presented to corroborate the effectiveness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time issues (finite-time stability, finite-time boundedness, finite-time H ∞ control) of discrete-time switched systems. Different from the existing Lyapunov function (LF) approaches only concerning activated subsystem, a novel approach for constructing LF is first proposed, which not only depends on the subsystem the switching reaches but also is closely related to the freshly inactive subsystem. Based on this, a transferring-dependent convex Lyapunov function (CLF) and a transferring-dependent LF are introduced, under which the improved finite-time stability results are deduced with admissible edge-dependent average dwell time (AED-ADT) technique. In light of the merits of established finite-time stability criteria, two transferring-dependent controllers are devised—that is, transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC)—to perform finite-time control synthesis. Then, the finite-time H ∞ control is further investigated based on the obtained control synthesis results. The designed transferring–dependent controllers can guarantee that the underlying system is finite-time bounded (FTB) with a prescribed H ∞ performance under tighter AED-ADT switching signals. Besides, it is the first time to use the multiple convex Lyapunov function (MCLF) to investigate the finite-time issues. Finally, two numerical examples and a practical example are used to verify the effectiveness of the developed results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of asynchronous control for a class of discrete-time switched systems is investigated under mode-dependent integrated dwell time (MDIDT) switching. By constructing a time-dependent convex function, a multiple convex Lyapunov function (MCLF) is firstly proposed for the asynchronous control of the switched systems. Under the MDIDT switching strategy, the matching interval is divided reasonably, and the convex function combination is constructed on the partitioned interval. Under asynchronous switching, the Lyapunov function is continuous when the subsystem mode is switched, but discrete when the controller mode is changed. Then, the increase of the Lyapunov function in the mismatched interval will be offset by the attenuation in the matched interval. In light of these merits, the stability results of the system are deduced, and the asynchronous controller is devised to guarantee the globally uniformly exponentially stability of the closed-loop system. Comparing with the traditional asynchronous control methods, the proposed method has less conservative results and larger stability regions. Finally, a numerical example and an application example are demonstrated to verify the validity and superiority of the asynchronous control scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the H ∞ filtering problem for a class of discrete-time switched systems by using an admissible edge-dependent average dwell time (AED-ADT) method. By means of a convex combination of positive definite matrices, a novel multiple piecewise convex Lyapunov function (MPCLF) is constructed, which can loosen the restrictions of Lyapunov function at switching points and interval interior points. Based on the MPCLF approach, sufficient conditions are established such that the filtering error system is globally uniformly exponentially stable (GUES) and a prescribed noise attenuation level in an H ∞ sense is achieved. Moreover, the corresponding time-varying H ∞ filters are given as well. Finally, the results of the simulation illustrate the feasibility and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The l 2 - l ∞ filtering problem is studied for a class of discrete-time switched systems under the admissible edge-dependent average dwell time (AED-ADT) switching. Firstly, a new multiple convex Lyapunov function (MCLF) is established as a convex combination form in the context of the l 2 - l ∞ filtering problem. Then, corresponding to the MCLF, the quasi-time-dependent switched filter is proposed for the considered switched system, and the sufficient conditions are derived to ensure that the filtering error system is globally uniformly exponentially stable with a prescribed l 2 - l ∞ performance index. Owing to the quasi-time-dependent and multi-degree-of-freedom properties of the designed switched filter, the wider feasibility regions of system parameters, more desirable l 2 - l ∞ disturbance attenuation levels and tighter bounds on the AED-ADT can be acquired. Finally, a numerical example is given to expound that our approach outperforms the extant results. [ABSTRACT FROM AUTHOR]

Abstract In this paper, the stability problem is investigated for a class of discrete-time switched systems with unstable subsystems under the mode-dependent average dwell time (MDADT) switching. A multiple convex Lyapunov function (MCLF) and a multiple piecewise convex Lyapunov function (MPCLF) are firstly proposed, which are formulated in a convex combination form of positive definite matrices with quasi-time-dependent coefficients. It is pointed out in the paper that the multiple Lyapunov function (MLF) and the multiple discontinuous Lyapunov function (MDLF) can be regarded as special cases of the proposed MCLF and MPCLF, respectively. Then, the exponential stability conditions are derived by the new Lyapunov functions. Both slow switching and fast switching are exerted on stable modes and unstable modes, respectively. Finally, two numerical examples are given to demonstrate that larger stability regions and tighter MDADT bounds can be obtained by using our developed techniques compared with some recent results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the stability and stabilization problems are considered for discrete-time switched systems in both nonlinear and linear contexts. By introducing the concept of forward average dwell time and using multiple-sample Lyapunov-like functions variation, the extended stability results for discrete-time switched systems in the nonlinear setting are first derived. Then, the criteria for stability and stabilization of linear switched systems are obtained via a newly constructed switching strategy, which allows us to obtain exponential stability results. A new kind of mode-dependent controller is designed to realize the stability conditions expressed by the multiple-sample Lyapunov-like functions variation. Based on this controller, the stabilization conditions can be given in terms of linear matrix inequalities (LMIs), which are easy to be checked by using recently developed algorithms in solving LMIs. Finally, a numerical example is provided to show the validity and potential of the results. [Copyright &y& Elsevier]

This paper investigates the H ∞ asynchronous filtering problem of discrete-time linear switched systems. A foreseeable Lyapunov function is firstly proposed for the asynchronous filtering error system with mode-dependent integrated dwell time (MDIDT) switching. The novelty consists in that the Lyapunov function carries the future state in the form of the convex linear functions which enables us to take into account the state and noise information at the next instant during the design process of the filter. The Lyapunov function follows the operation of the asynchronous filter and is designed corresponding to the partition of the synchronous intervals. In light of these merits, the stability and non-weighted l 2 -gain performance can be deduced, and then the foreseeable H ∞ asynchronous filter is devised to ensure the resulting filtering error system is globally uniformly exponentially stable (GUES) with a prescribed non-weighted l 2 -gain. The word foreseeable signifies that the H ∞ performance analysis of the filtering error system can't do without the noise knowledge at the next instant. Compared with the traditional filter design method, our method gets tighter bounds on the dwell time and smaller filtering error results. Finally, the effectiveness and superiority of our filtering scheme is verified by application examples. [ABSTRACT FROM AUTHOR]