Delay-Dependant Stability of Chaotic Systems with Exponential Synchronization

This study is concerned with the synchronization problem for a class of chaotic systems with multiple time-delays and transmitted noise. A dynamic compensator is proposed to achieve the synchronization between master and slave chaotic systems with multiple timedelays. First, the neural-network (NN) model is employed to approximate the chaotic systems with multiple time delays. Then, a linear differential inclusion (LDI) state-space representation is established for the dynamics of the NN model. Based on the LDI state-space representation, an exponential stability criterion of error dynamics derived in terms of Lyapunov's direct method is proposed to ensure that the trajectories of the slave system can approach those of master system. Subsequently, the stability condition of this criterion is reformulated into a linear matrix inequality (LMI). Based on the LMI, a fuzzy controller is synthesized to realize the exponential synchronization of the chaotic master-slave systems. Finally, this study provides a numerical example with simulations is given to illustrate the concepts discussed throughout this work.