A stochastic stabilization problem for a class of discrete-time switched linear singular system is considered in this paper. By using the Bernoulli variable, a kind of stochastic controller is developed, which ensures the discrete-time switched linear singular system stochastically stable. Based on a linear matrix inequality technology, a sufficient existence condition for such new controller i...

The paper investigates the realization problem for piecewise-affine discrete-time hybrid systems. A piecewise-affine discrete-time hybrid system is a discrete-time system such that the state-transition and readout maps are piecewise-affine maps. We will restrict our attention to autonomous systems and we will study the following realization problem. For a specified output trajectory, find a pie...

An exact condition for uniform stabilization and disturbance attenuation for switched linear systems is given in the discrete-time domain via the union of an increasing family of linear matrix inequality conditions. Associated with each Markovian jump linear system is a switched linear system, so we obtain a necessary and sufficient condition for almost sure uniform stabilization and disturbanc...

A powerful approach for analyzing the stability of continuous–time switched systems is based on using tools from optimal control theory to characterize the “most unstable” switching law. This reduces the problem of determining stability under arbitrary switching to analyzing stability for the specific “most unstable” switching law. More generally, this so–called variational approach was success...

This chapter aims to study the problem of stability analysis, and robust exponential stabilization for a class of switched linear systems with polytopic uncertainties is reviewed. A sufficient condition based on the average dwell time that guarantees the exponential stability of uncertain switched linear systems is given. First, the iterative learning control is presented to build a formulation...

This paper presents new sufficient conditions for exponential stability of switched linear systems under arbitrary switching, which involve the commutators (Lie brackets) among the given matrices generating the switched system. The main novel feature of these stability criteria is that, unlike their earlier counterparts, they are robust with respect to small perturbations of the system paramete...

The robust output regulation problem of switched linear multi-agent systems is studied in this paper. The dynamics of each agent are described by a switched linear system. According to the characteristics of agent network and switched systems, we put forward an agent-dependent average dwell time method. Owing to the limited information exchange between agents, distributed dynamic controllers ar...