Switching Delay Effects on Input-to-State Stability of Switched Systems

In this paper, input-to-state stability (ISS) is investigated for a class of nonlinear switched systems with time-varying switching delay, in which both ISS and non-ISS subsystems are considered simultaneously. By means of the Lyapunov function method, we show that ISS can be ensured for switched systems with time-varying switching delay if the activation time of ISS subsystems is sufficiently large and switching delays satisfy certain conditions. Moreover, inspired by (Zhang et al. 2020), a time-dependent multiple Lyapunov function is considered for linear switched systems with switching delay to obtain less conservative results, where the conservativeness can be reduced by explicitly providing the lower and upper bounds of switching intervals. Finally, simulations including an example of coordination of multiagent systems are offered to verify the effectiveness of the proposed results.