Delay Method Based Sos Polynomial Fuzzy Systems Control Synthesis And Applications

Recently, T-S fuzzy model has been extended to polynomial fuzzy model, which represents nonlinear systems more effectively. And sum-of-squares (SOS) approach has been applied to investigate the stability analysis and synthesis for the polynomial fuzzy control systems. However, the existing results on polynomial fuzzy systems do not involve in state time-delays.The paper mainly considers the stability analysis,H∞control and robust control problems for polynomial fuzzy continuous (discrete) systems with time-varying delay, by using the sum-of-squares (SOS) approach. Based on Lyapunov-Krasovskii stability theorem, through employing state-dependent Lyapunov-Krasovskii functional and introducing some free weighting matrices, delay-dependent stability criteria and the stabilization method which are based on parallel distributed compensation (PDC) are derived. Next, as for the robust stabilization problem, the controller is required to guarantee the asymptotic stability of the resulting closed-loop system, in spite of parameter uncertainties. On the other hand, in the H∞control design, it is apparent that the controller is required to guarantee the asymptotic stability of the closed-loop polynomial fuzzy system and achieve a H∞performance index. Finally, the sum-of-squares (SOS) approach is applied to study the synchronization of chaos.All the results in the paper are represented in terms of SOS, which can be efficiently solved via the recent developed Matlab toolbox SOSTOOLS. Simulation examples are given to verify the effectiveness and merits of the proposed approach.