Reduced-order Fuzzy Modeling for Nonlinear Switched Systems

In this paper, the problem of model approximation is investigated for T-S 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 also translates it into a lower-dimensional linear switched system. By 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.