An observer-based approach to controlling time-delay chaotic systems via Takagi–Sugeno fuzzy model

This study presents a fuzzy model-based control criterion for time-delay chaotic systems with uncertainty. The Takagi–Sugeno (T–S) fuzzy model is adopted for representing a chaotic system possessing a time delay. A unified approach for designing a fuzzy observer, which integrates parallel distributed compensation with an adaptive updating method, is first discussed. An observer-based fuzzy control scheme is then developed to deal with stabilization and tracking problems. Based on Lyapunov stability analysis, sufficient conditions that ensure robust control performance of time-delay chaotic systems are derived. These conditions are represented in terms of linear matrix inequalities and adaptive updating laws. Finally, the proposed approach is validated through numerical synchronization, stabilization, and model tracking control simulations.