Takagi–Sugeno fuzzy receding horizon H∞H∞ chaotic synchronization and its application to the Lorenz system

In this article, we propose a new H∞H∞ synchronization method for chaotic systems with external disturbance based on the Takagi–Sugeno (T–S) fuzzy model and receding horizon control. This synchronization method is called a Takagi–Sugeno fuzzy receding horizon H∞H∞ synchronization (TSFRHHS) method. A new set of matrix inequality conditions on the terminal weighting matrix is proposed for T–S fuzzy chaotic systems wherein non-increasing monotonicity of the optimal cost is guaranteed. Under this set of terminal inequality conditions, the proposed TSFRHHS method guarantees the infinite horizon H∞H∞ performance for T–S fuzzy chaotic systems with external disturbance. As an application of the proposed synchronization method, the TSFRHHS problem for the Lorenz system is investigated.