Fuzzy adaptive observer-based control for Chua??s circuit with output time delay

The authors present an H_∞ tracking performance design scheme via fuzzy adaptive observer-based control for chaotic Chua´s systems with output time delay. The Takagi´Sugeno-type fuzzy linear model with adaptation capability is used to approximate the chaotic system. Based on the fuzzy model, a two-layer fuzzy observer is used to reconstruct the system states according to output time delay. A state feedback controller is developed to override the non-linearities, time delays and external disturbances, while the linguistic information is utilised by setting the membership functions of fuzzy logical system and the adaptation parameters to estimate the model uncertainties and system states directly for using linear analytical results as the system states are unknown or partially known, and the system output is with delay. Based on Lyapunov criterion and linear matrix inequalities method, some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbance on the tracking error can be attenuated to any prescribed level and consequently an H_∞ tracking control is achieved. Finally, a chaotic Chua´s circuit system as a simulation example and some comparisons are given to illustrate the validity and effectiveness of the proposed method.