Asynchronous Switched Systems: ADT Switching

Abstract

This chapter first investigates the stability and \(l_2\)-gain analysis problems for a class of discrete-time switched systems with average dwell time (ADT) switching by allowing the Lyapunov-like functions to increase during the running time of subsystems. The obtained results then facilitate the studies on the issues of asynchronous control, where “asynchronous ” means the switching of the controllers has a lag to the switching of system modes. The basic asynchronous stabilization and asynchronous \(H_\infty \) control problem are both studied and the case for the system with time-varying parameter is further addressed under the modal average dwell time (MADT). Finally, the asynchronous \(H_\infty \) filter design problem is dealt with for the underlying switched linear systems with ADT switching. The phenomenon of “asynchronous” switching will unavoidably deteriorate the control performance such as the \(H_\infty \) noise attenuation index. However, it can be verified that the designed controller/filter considering the synchronous switching will be not necessarily valid in the presence of asynchronous switching. Several examples are provided to show the potential of the developed results.