An asymptotic stability theorem of Peuteman–Aeyels for Itô processes and its applications in synchronous switching systems

The paper studies the asymptotically stabilization of stochastic systems. First, an asymptotic stability theorem of Peuteman–Aeyels is extended from a deterministic setting to a stochastic framework. Second, a sufficient and necessary condition is proposed for the mean square stabilizability of linear stochastic systems via controller switching. Finally, a second-order example is delivered to illustrate the application of switching approach.