Stability Analysis And Control For Discrete T-S Fuzzy Descriptor Systems

The theory of descriptor systems is one of the important branches of moderncontrol theory. The theory of T-S fuzzy descriptor systems can deal with the analysisand design problems of nonlinear descriptor systems effectively. So far, only few workson discrete-time T-S fuzzy descriptor systems has been obtained. This paper discussesthe problems of stability analysis and control problems of discrete-time T-S fuzzydescriptor systems.Firstly, the admissibility conditions of fuzzy descriptor systems under the discreteconditions are studied. The key point of this part is to construct strict LMI admissibilityconditions. Based on a common Lypunov function and a fuzzy Lypunov function, newstrict LMI formulations to the admissibility conditions for unforced systems have beenobtained by slack variables technique respectively.Secondly, the stabilization problems for discrete-time T-S fuzzy descriptor systemshave been dealt with. Based on the new admissibility conditions, by introducing somesupplementary free variables, a new formulation which can be used directly to designcontrollers has been proposed. Then, the state feedback controller and static outputfeedback controller are discussed. The control conditions to uncertain T-S fuzzydescriptor systems are also given.Finally, the H∞control problem of a class of discrete-time T-S fuzzy descriptorsystems is discussed. Based on the new admissibility conditions present in this paper,the admissibility conditions with H∞performance have been derived by constructingan augmented system. Then, strict LMI formulation with intermediate variable isproposed. The proposed new formulation is more adapted to the H∞control problemdesign and less conservative. The analysis for designing a state feedback controller isdiscussed further.