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

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.