On exponential stability for linear switched stochastic systems: Multiple Lyapunov functions approach

We are interested in characterizing the effect of noise perturbation on the stability of switched systems. To this end, we extend the multiple Lyapunov functions approach to the linear Itô stochastic switched systems and make use of Itô formula to get almost sure exponential stability conditions. Furthermore, subsystem´s state-feedback control design is addressed aiming at making the closed-loop system almost sure exponentially stable, which is governed by some specified switching signal. An illustrative example is given to show the effectiveness of the results.