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

and Applied Analysis 3 established for the dynamics of the NNmodel. Next, in terms of Lyapunov’s direct method, a delay-dependent criterion is derived to guarantee the exponential stability of the error system between the master system and slave 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 ∞ performance by minimizing the disturbance attenuation level at the same time. The remainder of this paper is organized as follows. The system description is arranged in Section 2. In Section 3, a robustness design of fuzzy control and a delay-dependent stability criterion are proposed to realize the optimalH exponential synchronization. The design algorithm is given in Section 4. In Section 5, the effectiveness of the proposed approach is illustrated by a numerical simulation. Finally, the conclusions are drawn in Section 6. 2. Problem Formulation Consider two different multiple time-delay chaotic (MTDC) systems in master-slave configuration. The dynamics of the master system (N m ) and slave system (N s ) are described as follows: N m : . X (t) = f (X (t)) + g