Dissipativity based stability of switched systems with state-dependent switchings

Abstract

Stability problem of switched systems with state-dependent switchings is addressed. Sufficient conditions for stability are presented using dissipativity property of subsystems on their active regions. In these conditions, each storage function of a subsystem is allowed to grow on the “switched on” time sequence but the total growth is bounded in certain ways. Asymptotic stability is achieved under further assumptions of a detectability property of a local form and boundedness of the total change of some storage function on its inactive intervals. A necessary and sufficient condition for all subsystems to be dissipative on their active regions is given and a state-dependent switching law is designed. As a particular case, localized Kalman-Yakubovich-Popov conditions are derived for passivity. A condition for piecewise dissipativity property and a design method of switching laws are also proposed.