Integral input-to-state stability of switched delayed systems with delay-dependent impulses under generalized impulsive and switching scheme

Abstract

This paper studies integral input-to-state stability (iISS) of a class of hybrid delayed systems with impulse and switching behavior, in which the delay-dependent impulse and switching behavior are allowed for asynchronous occurrence. Relative to admissible edge-dependent average dwell time (AED-ADT) concept of the switching signal, a fresh concept of admissible edge-dependent average impulsive interval (AED-AII) is proposed for the impulse signal. Several sufficient criteria for iISS are achieved by using multiple Lyapunov–Krasovskii functional (MLKF) tool, AED-ADT switching, and AED-AII schemes. An improved inequality that describing the relation among Lyapunov function continuous switching signal and discrete impulse is constructed, where the jump amplitude at discrete switching points and impulsive moments including delay-dependent part and delay-independent part are involved. Compared with existing results, our conclusions have the following novelties: (1) the influence of time delay existing in continuous dynamics and discrete impulse on the function part of L-K functional is dug out, which is less conservative; (2) the AED-AII scheme proposed in this paper is combined with the AED-ADT switching method, which contains a larger set of the impulsive and switching signal. Moreover, the stability criterion is suitable for the arbitrary time delay in situation that all the subsystems are destabilizing. Finally, an example is given to verify the validity of the results.