Delayed-based H∞ tracking performance design for chaotic systems

In this paper, a delay-based H_∞ tracking performance scheme for chaotic systems with output delays is proposed. The Takagi and Sugeno fuzzy model with adaptation capability is employed to approximate the chaotic system. Based on the fuzzy model, a fuzzy observer-based controller is developed to achieve the H_∞ control performance when system with external disturbance rejection. The fuzzy adaptive observers consist of a two-layer fuzzy observer is used to reconstruct the system states cause by system with delayed output. Furthermore, the delayed time is partitioned and the fuzzy sub-observer is set at each partitioned time instant. Estimation errors and tracking errors can convergence to a bounded region by using the Lyapunov synthesis approach and linear matrix inequalities (LMIs) and the H_∞ tracking performance in the closed-loop system can be achieved. Finally, a Chua´s chaotic circuit system is used to verify the validity of theoretical derivations.