Unified stability criteria of asynchronous discrete-time impulsive switched delayed systems: bounded admissible edge-dependent average dwell time method

This article investigates input-to-state stability (ISS) problem of asynchronous discrete-time impulsive switched delayed systems, in which switching and impulse may be asynchronous. A novel bounded admissible edge-dependent average dwell time (BAED-ADT) switching signal is designed. Based on this division rule of switching subsystems, we adopt the slow switching method for the stable subsystems and the fast switching method for the unstable subsystems, so that stable subsystems can compensate unstable subsystems. Combined with admissible edge-dependent average impulsive interval (AED-AII) impulsive signal, a new unified ISS stability result is established, which could be applied to impulsive switched systems with an arbitrary combination of unstable and stable subsystems. Without solving the linear matrix inequality, it is allowed to readjust the AED-ADT boundary of the newly proposed stability condition according to the actual impulsive and switching signal. Further, compared with the existing fruits, the new stability condition is an extension and improvement of the previous one, which is less conservative. Several numerical examples are provided to show the validity of the conditions and the advantages of the theoretic results.