Dwell-time controllers for stochastic systems with switching Markov chain

We study the problem of feedback stabilization of a family of nonlinear stochastic systems with switching mechanism modeled by a Markov chain. We introduce a novel notion of stability under switching, which guarantees a given probability that the trajectories of the system hit some target set in finite time and remain thereinafter. Our main contribution is to prove that if the expectation of the time between two consecutive switching (dwell time) is “sufficiently large”, then the system is stable under switching with guaranteed probability. We illustrate this methodology by constructing measurement feedback controllers for a wide class of stochastic nonlinear systems.