Robust Control Research On Fuzzy Singular Systems With Time-Delay Based On LMI

With the continuous development of control theory, the control accuracy is demanded more and more highly. In recent years, time-delay which generally makes systems instability has been investigated gradually. Meanwhile, increasing attention has been focused on singular systems because they can better describe physical systems than the ordinary state space systems. On the other hand, fuzzy T-S model has been used more widely for its outstanding performance in processing on nonlinear and time-delay systems. Therefore, the analysis and synthesis of fuzzy singular systems with time delay are important both in theory and practice. Meanwhile, it has become a focus of research in control field. Currently, basic theories of fuzzy singular systems with time-delay have got certain achievement. However, the robust control theories of that need to be further developed and perfected.In this thesis, base on the Lyapunov stability theory, the linear matrix inequalities method and fuzzy T-S model, robust guaranteed cost control and robust H∞control of fuzzy singular system with time-delay are investigated. The main contents of this thesis are stated as follows:1, The robust H∞control of fuzzy singular time-delay system with disturbance is studied. Base on the linear matrix inequalities method and Lyapunov functional method, the stability and existing condition of H∞y sub-optimal state feedback control law of system are investigated. Robust sub-optimal state feedback controller is presented by solving the LMI. Numeric examples are provided to illustrate the effectiveness of the proposed method.2, The robust H∞of fuzzy singular uncertain system with time-delay is studied. Base on the linear matrix inequalities method and Lyapunov-Krasovskii functional method, the stability and existing condition of delay-dependent state feedback control law of system are investigated. Robust delay-dependent state feedback controller is presented by solving the LMI. Numeric examples are provided to illustrate the effectiveness of the proposed method. Moreover, compared with the existed results, the new method has lower conservative.3, The robust guaranteed cost control of fuzzy singular uncertain system with time-delay is studied. Base on the linear matrix inequalities method and Lyapunov functional method, the stability and existing condition of guaranteed cost control law of system are investigated. Robust guaranteed cost controller is presented by solving the LM1, which makes both closed-loop systems quadratic stable for all admissible uncertainties and guarantying cost function bounded in a limitation. Numeric examples are provided to illustrate the effectiveness of the proposed method.