Fuzzy modelling and impulsive control of the hyperchaotic Lü system

This paper presents a novel approach to hyperchaos control of hyperchaotic systems based on impulsive control and the Takagi–Sugeno (T–S) fuzzy model. In this study, the hyperchaotic Lu system is exactly represented by the T–S fuzzy model and an impulsive control framework is proposed for stabilizing the hyperchaotic Lu system, which is also suitable for classes of T–S fuzzy hyperchaotic systems, such as the hyperchaotic Rossler, Chen, Chua systems and so on. Sufficient conditions for achieving stability in impulsive T–S fuzzy hyperchaotic systems are derived by using Lyapunov stability theory in the form of the linear matrix inequality, and are less conservative in comparison with existing results. Numerical simulations are given to demonstrate the effectiveness of the proposed method.