Stability and stabilization of T-S fuzzy systems with time-varying delay: an input-output approach

Abstract

An input-output approach to the stability and stabilization of Takagi-Sugeno (T-S) fuzzy system with time-varying delay is proposed in this paper. A novel method is employed to approximate the time-varying delay. Thus the considered system can be formulated into a feedback interconnection form, which contains a constant time-delayed forward subsystem. Then based on the scaled small gain theorem, the problem reduces to studies of the bounded real property and H∞ control problem of the scaled forward subsystem. Some effective techniques used to be applied to the constant time delay systems are now utilized to solve the time-varying case. By virtue of this conversion, less-conservative stability criteria and stabilization methods via Parallel Distributed Compensation (PDC) scheme are obtained. Numerical experiments are performed to illustrate the advantage of the proposed techniques.