Fuzzy control systems design and analysis: a linear matrix inequality approach: Kazuo Tanaka and Hua O. Wang; Copyright John Wiley & Sons, Inc., 2001, ISBN: 0-471-32324-1

In this chapter, a class of nonlinear time-delay systems based on the TakagiŽ . w x Sugeno T-S fuzzy model is defined 1 . We investigate the delay-independent stability of this model. A model-based fuzzy stabilization design utilizing Ž . the concept of parallel distributed compensation PDC is employed. The main idea of the controller design is to derive each control rule to compensate each rule of a fuzzy system. Moreover, the problem of H control of this class of nonlinear time-delay systems is considered. The associated control Ž . synthesis problems are formulated as linear matrix inequality LMI problems. In the original T-S fuzzy model formulation, there is no delay in the control and state. However, time delays often occur in many dynamical systems such as biological systems, chemical systems, metallurgical processing systems, and network systems. Their existence is frequently a cause of instability and poor performance. The study of stability and stabilization for w x linear time-delay systems has received considerable attention 2 6 . But these efforts were mainly restricted to linear time-delay systems. Thus, it is important to extend the stability and stabilization issues to nonlinear time-delay systems. In this chapter, a particular class of nonlinear time-delay systems is introduced based on the Tagaki-Sugeno fuzzy model. This kind of nonlinear system is represented by a set of linear time-delay systems. We will call this a Ž . T-S model with time delays T-SMTD . In the literature, the problem of stability and stabilization of time-delay systems has been dealt with a number of different ways. There are some results that are independent of the size of w x the time delays in 2 4 , and the stability is satisfied for any value of the time delays. There are also some delay-dependent results, in which the stability is