Stochastic incremental H∞ control for discrete-time switched systems with disturbance dependent noise

Abstract In this paper, the (reverse)mode-dependent average dwell time ((reverse)MDADT) scheme incorporated with multiple incremental Lyapunov functions are utilized to investigate the incremental H∞ control for nonlinear discrete-time stochastic switched systems (SSS). The sufficient conditions in terms of (reverse)MDADT for the incremental H∞ control are derived such that an incrementally globally asymptotically stable in the mean (IGASiM) system with a prescribed H∞ disturbance attenuation level is obtained. It is shown that an incremental H∞ control could be attained when all of the subsystems are non-IGASiM. Moreover, when the discrete-time SSS is composed of some IGASiM and non-IGASiM subsystems, a (reverse)MDADT based relationship between these two kinds of subsystems is established such that an IGASiM discrete-time SSS with incremental L2-gain property is obtained. Two numerical examples are presented to demonstrate the effectiveness of the results.