FUZZY OBSERVER DESIGN In practical applications, the state of a system is often not readily available. Under such circumstances, the question arises whether it is possible to determine the state from the system response to some input over some period of time. For linear systems, a linear observer w1x provides an affirmative answer if the system is observable. Likewise, a systematic design method of fuzzy regulators and fuzzy observers plays an important role for fuzzy control systems. | Fuzzy Control Systems Design and Analysis A Linear Matrix Inequality Approach Kazuo Tanaka Hua O. Wang Copyright 2001 John Wiley Sons Inc. CHAPTER 4 ISBNs 0-471-32324-1 Hardback 0-471-22459-6 Electronic FUZZY OBSERVER DESIGN In practical applications the state of a system is often not readily available. Under such circumstances the question arises whether it is possible to determine the state from the system response to some input over some period of time. For linear systems a linear observer 1 provides an affirmative answer if the system is observable. Likewise a systematic design method of fuzzy regulators and fuzzy observers plays an important role for fuzzy control systems. This chapter presents the concept of fuzzy observers and two design procedures for fuzzy observer-based control 2 3 . In linear system theory one of the most important results on observer design is the so-called separation principle that is the controller and observer design can be carried out separately without compromising the stability of the overall closed-loop system. In this chapter it is shown that a similar separation principle also holds for a large class of fuzzy control systems. FUZZY OBSERVER Up to this point we have mainly dealt with LMI-based fuzzy control designs involving state feedback. In real-world control problems however it is often the case that the complete information of the states of a system is not always available. In such cases one need to resort to output feedback design methods such as observer-based designs. This chapter presents fuzzy observer design methodologies involving state estimation for T-S fuzzy models. Alternatively output feedback design can be treated in the framework of dynamic feedback which is the subject of Chapter 12. 83 84 FUZZY OBSERVATION DESIGN As in all observer designs fuzzy observers 4 are required to satisfy x t - x t 0 as t to where x t denotes the state vector estimated by a fuzzy observer. This condition guarantees that the .
