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A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper.The T-S fuzzy model is employed to represent the systems.First,the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling.Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability.Finally,the error caused by fuzzy modeling is considered and the input-to-state stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error.By the small-gain theorem,the resulting closed-loop system is proved to be input-to-state stable.Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded.The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.
A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. TS fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Percentage with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability .Finally, the error caused by fuzzy modeling is considered and the input-to-state stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to- state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. the effectiveness of the proposed controller design methodology is tested through numerical simulation on the chaotic Henon system.