Dissipativity Analysis and Synthesis for a Class of T–S Fuzzy Descriptor Systems

Abstract

This paper is concerned with the problems of dissipativity analysis and synthesis for a class of Takagi–Sugeno (T–S) fuzzy descriptor systems with different derivative matrices. First, a new augmented system which is equivalent to the original system is given to deal with these different derivative matrices. By employing a fuzzy Lyapunov function and slack matrices, a set of relaxed sufficient conditions are developed to guarantee that the unforced systems are admissible (regular, impulse free, and stable), which includes the existing related results as special cases. The developed conditions are expressed in terms of strict linear matrix inequalities (LMIs), which is convenient for checking the admissibility. Then, a novel method is proposed to design an admissible fuzzy controller. Second, by applying the dissipativity theorem and Lyapunov stability theorem, a set of sufficient conditions are derived to ensure that the resultant closed loop systems are admissible and dissipative, and the fuzzy controllers are designed using LMIs techniques. Finally, some examples are provided to illustrate that the main results in this paper are feasible and less conservative than the earlier related ones.