Stability of state-dependent switched systems under hybrid delayed impulsive control

In this paper, a novel state-dependent switching (SDS) method for switched systems with hybrid delayed impulses is proposed, which is different from the conventional approach of pre-setting the switching instants. First, for the SDS method involving delayed impulses, two preconditions, namely, coverage and overlap, are guaranteed. Then, by the Lyapunov stability theory and the proposed SDS strategy, the unified stability criteria of the switched systems under hybrid delayed impulsive control are obtained. Moreover, we discover that the impulsive delay has a double effect, that is, undermining and promoting system stability, which is contingent on the stability of the original systems. To validate the effectiveness of our results, we provide illustrative examples involving circuit switched networks.