Robust stabilization of switched linear systems with Wiener process noise

A constructive approach to robust stabilization of switched systems subject to a Wiener process noise is presented. The uncertainties in the system are assumed to be sector bounded. Multiple Lyapunov functions are employed to develop sufficient conditions for a switched stochastic system to be stable in the mean square sense. The stability criterion is expressed in terms of existence of solutions to a set of linear matrix inequalities. State feedback design procedure is proposed to determine a switching rule and a set of associated feedback controller that robustly stabilizes the closed-loop system. A practical application related to the control of stochastic oscillators is provided to show the effectiveness of the proposed approach.