Passivity Control For T-s Fuzzy Descriptor Systems

This thesis is concerned with the problem of passivity control for a kind of time-delay T-S fuzzy descriptor systems by using the method of linear matrix inequality (LMI). The phenomenon of time-delay is widespread in the practical engineering, and the time-delay often leads to unstable or poor performance of the control systems. Therefore, the research of the robust control of the systems with time-delay both in the theory and in the practice are important. As the descriptor systems theory is widely used in the dynamic systems and the general space-perturbation theory and other fields, the research of the stability, the passivity and the robust control for descriptor systems with time-delay has become a hot topic in recent years. Time-delay descriptor systems are nonlinear control systems, T-S fuzzy model just can be used to approximate or to describe a nonlinear system. Even though the research of the passive control for T-S fuzzy systems has yielded some results, passive control problem for T-S fuzzy descriptor systems with time-delay is still rare, so we study the problems in this thesis.In the first chapter, the fuzzy control of classification, characteristics, development history, current research and application are introduced.In the second chapter, the theoretical basis of fuzzy control systems is systematic introduced, including the fuzzy math, the basic theory of fuzzy control, fuzzy controller structure and the fuzzy control algorithm. Then, the stability analysis for hybrid fuzzy systems, language-based fuzzy systems and the sufficient condition is proposed.In the third chapter, the problem of passivity control for a kind of T-S fuzzy descriptor systems with time-delay is concerned. The sufficient conditions, which make the closed-loop system be admissible and strictly passive, are obtained for the systems. The conditions are expressed as linear matrix inequalities, so the feedback gain matrix can be obtained by solving the LMIs. An illustrative example is given to show the validity and feasibility of the proposed approach.In the fourth chapter, based on the previous presentation, the more universal time-varying delay T-S fuzzy descriptor systems passive control problem is discussed. Finally, examples are given to illustrate the method is feasible and more effective.In the fifth chapter, we summarize the status of fuzzy control and put forward the prospects of further research work.