Fuzzy Robust H₂ Guaranteed Cost Control Of Uncertain Nonlinear Systems

In this paper, by using fuzzy technique, the system stability and H₂ guaranteed cost control problem for uncertain nonlinear systems are researched. Fuzzy Takagi-Sugeno?T-S? models are used to model the nonlinear systems. Sufficient conditions for the existence of the fuzzy controllers are given in terms of linear matrix inequalities?LMIs?. Based on the Lyapunov stability theorem, the desired H₂ guaranteed cost control performance is analysed in the sense that the closed-loop systems are stable.Firstly, the system stability and H₂ guaranteed cost control for uncertain nonlinear systems are discussed. T-S fuzzy model is used to model the nonlinear systems, where the modeling error is assumed to be with the upper bound constraint. Applying the Lyapunov stability theorem and LMI technique, a sufficient condition for the system stability is given and the desired H₂ guaranteed cost performance is also guaranteed.The experimental results of the inverted pendulum system are given to illustrate the feasibility of the proposed control scheme.Secondly, the system stability and H₂ guaranteed cost control for uncertain nonlinear time-delay systems are researched. Time-delay T-S fuzzy model is employed to represent the nonlinear time-delay systems, where the modeling error is assumed to be with the upper bound constraint. The feedback is designed by using the parallel distributed compensation algorithm. Stability and H₂ guaranteed cost performance of the closed-loop system is proved by Lyapunov stability theory.Simulation results of chaotic systems demonstrate the effectiveness.Finally, the system stability and H₂ guaranteed cost control for uncertain nonlinear time-varying delay systems are discussed. The system is modeled by T-S fuzzy model with time varying delay, and the uncertainties satisfy matching conditions. By selecting the Lyapunov function, the stability of the system is proved and the H₂ guaranteed cost performance is ensured. The simulation experiment of chaotic system shows that the control scheme can achieve the desired H₂ performance.