Dissipativity Analysis and Synthesis for a Class of T–S Fuzzy Descriptor Systems
针对具有不同导数矩阵的T-S模糊描述符系统，提出基于模糊Lyapunov函数和松弛矩阵的耗散性分析与控制器设计方法，通过严格线性矩阵不等式条件保证系统可容许且耗散，算例表明结果比现有方法更少保守性。
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.