Input-Output Finite-Time Stability of Discrete-Time Impulsive Switched Linear Systems with State Delays

Abstract

This paper is concerned with the problem of input-output finite-time stability (IO-FTS) for discrete impulsive switched systems with state delays. Sufficient conditions are presented for the existence of IO-FTS for such systems under the cases of certain switching, arbitrary switching, and uncertain switching. All the obtained results are formulated in a set of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness of the proposed results.

Controller synthesis for constrained discrete-time switched positive linear systems

“…Assume the system state does not jump at the switching instants. Switched systems with state jumps are called impulsive systems or switched impulsive systems in the literature [38][39][40][41].…”

Exponential stability of impulsive positive switched systems with discrete and distributed time‐varying delays

“…During the operation of a dynamic system, the system behavior is not only possible to encounter the effect of time delay but also encounter the effect of impulse. Recently, stability problems of impulsive switched systems have been studied in other works . Moreover, there are also some results in the framework of positive systems .…”

“…In order to realize computer simulation and digital implementation of continuous time system better, the study of discrete‐time systems is receiving more and more attention of researchers . However, to the best of our knowledge, there is no paper focus on exponential stability problem of discrete‐time impulsive positive switched systems with mixed time‐varying delays.…”

Input-output finite-time stability of time-delay systems and its application to active vibration control

“…The authors studied the problems of IO-FTS analysis and synthesis for stochastic Markovian jump systems in [20]. The literature [21] addressed the problem of IO-FTS analysis for discretetime impulsive switched systems with time-invariant state delay. Sufficient conditions are obtained for IO-FTS of the system under the different cases of the switching signal.…”