Model Approximation for Fuzzy Switched Systems With Stochastic Perturbation

In this paper, the model approximation problem is investigated for a Takagi-Sugeno fuzzy switched system with stochastic disturbance. For a high-order considered system, our attention is focused on the construction of a reduced-order model, which not only approximates the original system well with a Hankel-norm performance but translates it into a lower dimensional fuzzy switched system as well. By using the average dwell time approach and the piecewise Lyapunov function technique, a sufficient condition is first proposed to guarantee the mean-square exponential stability with a Hankel-norm error performance for the error system. The model approximation is then converted into a convex optimization problem by using a linearization procedure. Finally, simulations are provided to illustrate the effectiveness of the proposed theory.