FUZZY DESCRIPTOR SYSTEMS AND CONTROL This chapter deals with a fuzzy descriptor system defined by extending the original Takagi-Sugeno fuzzy model. A number of stability conditions for the fuzzy descriptor system are derived and represented in terms of LMIs. A motivating example for using the fuzzy descriptor system instead of the original Takagi-Sugeno fuzzy model is presented. An LMI-based design approach is employed to find stabilizing feedback gains and a common Lyapunov function. | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTER 10 ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic FUZZY DESCRIPTOR SYSTEMS AND CONTROL This chapter deals with a fuzzy descriptor system defined by extending the original Takagi-Sugeno fuzzy model. A number of stability conditions for the fuzzy descriptor system are derived and represented in terms of LMIs. A motivating example for using the fuzzy descriptor system instead of the original Takagi-Sugeno fuzzy model is presented. An LMI-based design approach is employed to find stabilizing feedback gains and a common Lyapunov function. The descriptor system which differs from a state-space representation has generated a great deal of interest in control systems design. The descriptor system describes a wider class of systems including physical models and nondynamic constraints 1 . It is well known that the descriptor system is much tighter than the state-space model for representing real independent parametric perturbations. There exist a large number of papers on the stability analysis of the T-S fuzzy systems based on the state-space representation. In contrast the definition of a fuzzy descriptor system and its stability analysis have not been discussed until recently 2 . In 2 we introduced the fuzzy descriptor systems and analyzed the stability of such systems. This chapter presents both the basic framework of 2 3 as well as some new developments on this topic. As mentioned in Chapter 1 ht lvk 0 denotes all the pairs i k excepting ht z t vk z t 0 for all z t h l hj lvk 0 denotes all the pairs i j k excepting hi z t hj z t vk z t 0 for all z t and i j . h l hj lvk 0 denotes all i j excepting h z t hj z t vk z t 0 Vz t . 195 196 FUZZY DESCRIPTOR SYSTEMS AND CONTROL FUZZY DESCRIPTOR SYSTEM In 4 5 a fuzzy descriptor system is defined by extending the T-S fuzzy model and . The ordinary Takagi-Sugeno .
