Delayed-based fuzzy adaptive observer control design for nonlinear dynamic systems

In this paper, a delayed-based fuzzy adaptive observer control design method for a class of nonlinear output-delayed single-input single-output systems with guaranteed control performance is proposed. First, the Takagi and Sugeno fuzzy model is employed to approximate a nonlinear system. Next, based on the fuzzy model, a delayed based fuzzy adaptive observer using state feedback controller is developed to achieve the H_∞ tracking performance. The fuzzy adaptive observers consist of a serial-observation algorithm to reconstruct the system states at different delayed time instants for state estimation. Based on the Lyapunov synthesis approach, the state estimation errors are uniform ultimate boundedness property (UUB) and H_∞ tracking performance in the closed-loop system can be achieved. Finally, a Chua´s chaotic circuit system is used to illustrate the effectiveness of the proposed method.