Researches On Robust Fuzzy Control For A Class Of Nonlinear Descriptor Systems With Time Delays  Posted on:20090922  Degree:Doctor  Type:Dissertation  Country:China  Candidate:W H Tian  Full Text:PDF  GTID:1118360308978450  Subject:Control theory and control engineering  Abstract/Summary:  PDF Full Text Request  TS fuzzy descriptor system model which can approximate a nonlinear descriptor system perfectly, is thought to be an effective approach to solve the control problem of nonlinear descriptor systems. Currently, although much effort has been made in the exploration of stability analysis and control for the TS fuzzy descriptor system, the results on this topic are far fewer than those on normal systems. The research on TS 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 TS 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 TS 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 TS fuzzy descriptor model, the quadratic stability is studied by using Lyapunov stability theory and LMIs technology. Based on the quadratic stability, the robust Hâˆžcontrol method is proposed. The quadratic stability conditions and the sufficient conditions of the existence of robust Hâˆžcontroller are given in terms of LMIs. Next, Robust guaranteed cost control for uncertain TS 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 Hâˆžcontroller and robust guaranteed cost controller.3. Based on delaydependent method, the robust guaranteed cost control of a class of uncertain continous time nonlinear descriptor delay systems described by TS fuzzy descriptor model is investigated. The relationship between the size of delay and stability is discussed. And the estimation of the upper bound of delayÏ„max is formulated by a convex optimization problem. The minimized guaranteed cost upper bound corresponding toÏ„max 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 delaydependent method, the nonfragile Hâˆžcontrol problem of a class of uncertain continous time nonlinear descriptor delay systems described by TS fuzzy descriptor model is considered. First, a new delaydependent Hâˆžstability criterion is proposed aiming at the normal system. Then, based on two kinds of gain variations, the design methods of nonfragile controllers satisfying Hâˆžnorm bound are provided. The sufficient conditions of the existence of nonfragile Hâˆžcontroller are given in terms of LMIs. The simulation example indicates the effectiveness of the proposed method.5. A multiple delay TS fuzzy descriptor model is proposed. Based on Lyapunov stability theory and delayindependent method, guaranteed cost control and Hâˆžcontrol problems of a class of multiple delay nonlinear descriptor systems described by multiple delay TS fuzzy descriptor model are studied. The stability conditions and the sufficient conditions of existence of guaranteed cost controller and Hâˆžcontroller are given in terms of LMIs. I is worth noting that multiple delay TS fuzzy descriptor system is extension of single delay TS 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 TS 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.  Keywords/Search Tags:  fuzzy descriptor system, nonlinear descriptor system, fuzzy control, TSfuzzy descriptor system, time delay system, linear matrix inequalities(LMIs), guaranteed cost control, optimal control robust control, H_âˆžcontrol, nonfragile H_âˆžcontrol  PDF Full Text Request  Related items 
 
