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

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 H1 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.