Feedback control of switched stochastic systems using uniformly sampled mode information

Feedback stabilization of continuous-time switched linear stochastic dynamical systems is explored. The mode signal, which characterizes the switching between subsystems, is modeled as a Markov chain. We propose a feedback control law that depends only on the uniformly sampled mode information rather than the actual mode signal. We analyze the probabilistic dynamics of the sampled mode information, and develop a form of strong law of large numbers to show the almost sure asymptotic stability of the closed-loop system under the proposed control law. Finally, we present a numerical example to illustrate the efficacy of our approach.