Exponential convergence of multi-dimensional stochastic mechanical systems with switching

This research stems from a control problem for a suspension device. For a general switching stochastic mechanical system with a closed-loop control we establish under the linear growth condition on coefficients, that: 1) there exists a unique solution of the system, with a strong Markov property; 2) a mixing condition in the local Markov-Dobrushin form holds; 3) the system is exponentially stochastic stable.