Exponential stabilisation of impulsive switched linear systems via a periodic switching scheme

Abstract

In this study, the authors investigate the stabilisation issue for a class of multi‐module impulsive switched linear systems in terms of a periodic impulsive switching scheme. First, they establish a necessary and sufficient criteria on periodically exponentially (PE) stabilising the involved system. Then, they derive some effective asymptotic stabilisation and input‐to‐state stabilisation results using the method of construction. To improve the system performance, they solve an optimisation problem that determines the minimal period of stabilisable impulsive switching signals. Finally, a numerical example with two unstable subsystems is provided to illustrate the validity of the method.