A descriptor system approach to fuzzy control system designs using fuzzy Lyapunov function

This paper presents a descriptor system approach to fuzzy control system designs using fuzzy Lyapunov function. The redundancy of descriptor systems achieves reduction of the number of linear matrix inequality (LMI) conditions that directly relates to computational requirement. To derive more relaxed LMI conditions, we propose new types of fuzzy controller and fuzzy Lyapunov function. A main feature of the LMI conditions derived in this paper is to be able to consider feasibility of the LMIs according to the switching speed of each linear subsystems (exactly speaking, according to the lower bound of time derivative of membership functions). The first example shows that the LMI conditions based on the fuzzy Lyapunov function are less conservative than those based on a common (standard) Lyapunov function. The second example illustrates the utility of the fuzzy Lyapunov function approach for another piecewise Lyapunov function approach