Researches On Robust Fuzzy Control For A Class Of Nonlinear Descriptor Systems With Time Delays

T-S fuzzy descriptor system model which can approximate a non-linear descriptor system perfectly, is thought to be an effective approach to solve the control problem of non-linear descriptor systems. Currently, although much effort has been made in the exploration of stability analysis and control for the T-S fuzzy descriptor system, the results on this topic are far fewer than those on normal systems. The research on T-S fuzzy descriptor system is still in primary stage. Lots of problems need to be solved. In this paper, by using the advanced matrix theory and the linear matrix inequality (LMIs) technique, we study the problems of stability analysis and control design for a class of T-S fuzzy descriptor systems under the framework of Lyapunov stability theory, which is motivated by the linear descriptor system theory and advanced robust control theory. The main contributions are as follows:1. The problems of guaranteed cost control of a class of continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model are studied. First, sufficient conditions of the existence of state feedback guaranteed cost controller are given in terms of LMIs. Then fuzzy rule weights and some new variables are used to obtain an improved guaranteed cost controller design method which is less conservative. And design of guaranteed cost controller with minimized J0 is reduced to a convex optimization problem constrained by LMIs. A numeric example is provided to illustrate the effectiveness of the proposed method. At last, the problem of generalized observer based output feedback guaranteed cost control is discussed. The sufficient conditions of the existence of observer based output feedback guaranteed cost controller are given in terms of LMIs.2. Aiming at a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model, the quadratic stability is studied by using Lyapunov stability theory and LMIs technology. Based on the quadratic stability, the robust H∞control method is proposed. The quadratic stability conditions and the sufficient conditions of the existence of robust H∞controller are given in terms of LMIs. Next, Robust guaranteed cost control for uncertain T-S fuzzy descriptor delay system is discussed. And design of guaranteed cost controller with minimized J0 is reduced to a convex optimization problem constrained by LMIs. numeric examples are provided to illustrate the effectiveness of the proposed methods of robust H∞controller and robust guaranteed cost controller.3. Based on delay-dependent method, the robust guaranteed cost control of a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model is investigated. The relationship between the size of delay and stability is discussed. And the estimation of the upper bound of delayτmax is formulated by a convex optimization problem. The minimized guaranteed cost upper bound corresponding toτmax is reduced to an optimization problem of searching for the suboptimal value. The simulation results indicate the effectiveness of the proposed method.4. Based on delay-dependent method, the non-fragile H∞control problem of a class of uncertain continous time nonlinear descriptor delay systems described by T-S fuzzy descriptor model is considered. First, a new delay-dependent H∞stability criterion is proposed aiming at the normal system. Then, based on two kinds of gain variations, the design methods of non-fragile controllers satisfying H∞norm bound are provided. The sufficient conditions of the existence of non-fragile H∞controller are given in terms of LMIs. The simulation example indicates the effectiveness of the proposed method.5. A multiple delay T-S fuzzy descriptor model is proposed. Based on Lyapunov stability theory and delay-independent method, guaranteed cost control and H∞control problems of a class of multiple delay nonlinear descriptor systems described by multiple delay T-S fuzzy descriptor model are studied. The stability conditions and the sufficient conditions of existence of guaranteed cost controller and H∞controller are given in terms of LMIs. I is worth noting that multiple delay T-S fuzzy descriptor system is extension of single delay T-S fuzzy descriptor system. It is of more extensive practical significance, and has not been studied in other literature yet.6. The control problems of a class of discrete time nonlinear descriptor delay systems described by the discrete time T-S fuzzy descriptor model are considered. First, the definitions of consistent regularity, cause and effect, stability and admissibility are given. Then, The stability of the system is analyzed based on Lyapunov method. The sufficient conditions of the system to be consistent regular, cause and effect and stable are given in terms of LMIs. At last, design methods of state feedback and output feedback controllers are proposed.