Input-to-state stability for discrete hybrid time-delay systems with admissible edge-dependent average dwell time

Abstract

The input-to-state stability (ISS) for a class of discrete hybrid time-delay systems with admissible edge-dependent average dwell time (AED-ADT) is investigated in this study. By using the Lyapunov-like functions, the conditions for ISS are derived under the following situations: all subsystems are stable, all subsystems are unstable, and some subsystems are unstable. When all the continuous subsystems are ISS, although the impulsive effects are destabilizing, the system is ISS with respect to a lower bound of AED-ADT. Moreover, when all the subsystems are not ISS, the impulsive effects can still successfully stabilize the system for an upper bound of AED-ADT. When some continuous subsystems are not ISS, the impulsive effects can also successfully stabilize the system with a lower bound of AED-ADT under specific conditions. For the special case in which the Lyapunov-like function is allowed to decrease and increase during the operation time of a certain mode, a fresh transformation scheme of the Lyapunov-like functions is used to address the difficulty caused by the external input. A connection is established among AED-ADT, impulses magnitude, the interval length of increase of the Lyapunov function, and decaying/increasing rates of the Lyapunov function, such that the impulsive switched delayed system is ISS. The conclusions can be applied to a large class of systems because the transformation technique fills the gap between special and general cases. Finally, an example is provided, and simulations are performed to confirm the validity of the main results.