Delay-Dependent Exponential Optimal H ∞ Synchronization for Nonidentical Chaotic Systems via Neural-Network-Based Approach

Abstract

A novel approach is presented to realize the optimal $H^{\infty }$ exponential synchronization of nonidentical multiple time-delay chaotic (MTDC) systems via fuzzy control scheme. A neural-network (NN) model is first constructed for the MTDC system. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on this LDI state-space representation, a delay-dependent exponential stability criterion of the error system derived in terms of Lyapunov's direct method is proposed to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). According to the LMI, a fuzzy controller is synthesized not only to realize the exponential synchronization but also to achieve the optimal $H^{\infty }$ performance by minimizing the disturbance attenuation level at the same time. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.