Stabilization of switched linear systems with Wiener process disturbances

This paper is concerned with the control of switched systems with Wiener process disturbances. Based on multiple Lyapunov function approach and using a class of Metzler matrices, a new criterion is established to test the mean square stability by solving linear matrix inequalities (LMIs). A design procedure is then proposed to determine a switching rule that employs only the available feedback information, and an associated state feedback controller that, when applied simultaneously, stabilize the closed-loop system in mean square sense. A practical application related to the control of stochastic oscillators is provided to show the effectiveness of the proposed method.