Stochastic bounded real lemma for switched stochastic systems with average dwell time

This paper addresses the H∞ performance and H∞ control of switched stochastic linear systems subject to average dwell-time switching. At first, a sufficient condition is presented to guarantee the switched stochastic system to achieve a weighted H∞ performance under the condition that all subsystems are asymptotic mean square stable. Further, the disturbance attenuation property of the considered systems is investigated when both stable and unstable subsystems are included. It is shown that if the active time of unstable subsystems is properly allocated, a stochastic bounded real lemma (SBRL) can be established based on the solvability of linear matrix inequalities (LMIs). As an application of the obtained SBRL, the robust control problem is settled for a class of switched stochastic systems with (x,u,v)-dependent noises, and the state-feedback H∞ controller is developed.