Stabilty Analysis And Synthesis For Takagi-Sugeno Fuzzy Systems With Time-Delays

With the development of science, technology and productivity, the controlled paints are becoming more and more complex. For lack of accurate mathematical model, and there exist various nonlinear sections, uncertain to investigate the stability synthesis and control problem of nonlinear time delay systems. However there is no efficient method to solve this class of problems. As we know, T-S fuzzy model can approximate nonlinear systems significantly, and it is easy for us to analyze. T-S fuzzy control method has been the hotspots in the investigation of nonlinear systems. In this paper, the stability analysis and control problems of nonlinear time delay systems have been investigated based on T-S fuzzy model.First, a class of continuous T-S fuzzy uncertain systems with time-varying delay are studied. Based on Lyapunov-Krasovskii(L-K) approach ,the sufficient stability conditions are proposed, and then fuzzy controller is designed via parallel distribute compensation technique to stabilize the plant. The closed-loop system is asymptotically stable with the guaranteed cost performance and results in a minimal upper bound of the closed-loop value of cost function. Simulation results show the effectiveness of the proposed method.Second, the problem of the fuzzy state feedback control for a class of uncertain nonlinear systems with input and state time delay was addressed. The uncertain T-S fuzzy model with time delay was adopted for fuzzy modeling nonlinear system. The systematic design procedure based on LMI for the fuzzy robust controller design were given and some conditions were derived for the existence of fuzzy state feedback controllers such that the closed-loop system was asymptotically stable and the effect of the disturbance input on the controlled output was reduced to prescribed level and satiate H~∞norm bound constraint. Third, the problem of fuzzy modeling for uncertain time-delay nonlinear systems by fuzzy T-S model is addressed. On the basis of the fuzzy modeling, fuzzy feedback control and output feedback control developed. Sufficient conditions are derived for robust stabilization in the sense of Lyapunov asymptotic stability and formulated in the form of linear matrix inequalities (LMI), which can be efficiently solved with LMI optimization techniques.Next, considering uncertain forms, the robust adaptive resilient controller designs are presented. By adaptive approach, the controller design can be tuned on-line. A new memory state feedback strategy is addressed for a class of uncertain fuzzy systems with time-delay. An adaptive controller is given in the case of unavailable time-delay. The designed controller guaranteed controller guarantees the closed-loop system to be asymptotically stable and possesses good operation.In the end, the problem of decentralized fuzzy state-feedback controller design for a class of nonlinear interconnected large-scale systems with control and state time-delay is considered based on the T-S fuzzy models. The stabilizing conditions of closed-loop fuzzy system are obtained and the decentralized fuzzy state-feedback controller is designed through Lyapunov stability analysis theory and linear matrix inequality respectively. Based on that, for the first time, the resilient controller is designed by adaptive control approach for a class of fuzzy modeling of the interconnected large-scale systems, thus reducing the systems' fragility and strengthening robust.