Reduced-Order Model Approximation of Switched Systems

Abstract

This chapter considers the reduced-order model approximation issue for discrete hybrid switched nonlinear systems through T-S fuzzy modelling. We attempt to establish a reduced-order model for a high-dimension hybrid switched system, which can approximate the original high-order model subject to the prescribed system performance index. First, the mean-square exponential stability conditions are formulated to ensure the specific $\mathcal {H}_{\infty }$ performance for the resulting dynamic error system via the efficient Lyapunov stability method and ADT approach. The solutions of the relevant model reduction problems are derived using the projection technique, through which the algorithms of the reduced-order model parameters are established using a CCL method.