Feedback Control of Switched Stochastic Systems Using Randomly Available Active Mode Information

Abstract: Almost sure asymptotic stabilization of a discrete-time switched stochastic system is investigated. Information on the active operation mode of the switched system is assumed to be available for control purposes only at random time instants. We propose a stabilizing feedback control framework that utilizes the information obtained through mode observations. We first consider the case where stochastic properties of mode observation instants are fully known. We obtain sufficient asymptotic stabilization conditions for the closed-loop switched stochastic system under our proposed control law. We then explore the case where exact knowledge of the stochastic properties of mode observation instants is not available. We present a set of alternative stabilization conditions for this case. The results for both cases are predicated on the analysis of a sequence-valued process that encapsulates the stochastic nature of the evolution of active operation mode between mode observation instants. Finally, we demonstrate the efficacy of our results with numerical examples.