Stabilization of continuous-time switched linear stochastic systems

This paper addresses the problem of characterizing a switching strategy for stabilization of switched linear stochastic systems with state-dependent noise. The strategy is based on the determination of a minimum dwell time. Sufficient conditions that assure exponential mean square stability and a guaranteed cost-to-go performance index are established by analyzing the time evolution of the second-order moment of the state and constructing a novel cross-monotonicity condition at the switching instants, respectively. Alternative conditions are derived for numerical implementations. The proposed method is illustrated by numerical simulations.