Exponential synchronization of discontinuous chaotic systems via delayed impulsive control and its application to secure communication

• A general model for discontinuous chaotic systems with or without time-varying delay is proposed.
• Global exponential synchronization of the proposed model is studied.
• An uniform impulsive controller with multiple unknown time-varying delays is designed.
• Apply the obtained results to secure communication.

This paper investigates drive-response synchronization of chaotic systems with discontinuous right-hand side. Firstly, a general model is proposed to describe most of known discontinuous chaotic system with or without time-varying delay. An uniform impulsive controller with multiple unknown time-varying delays is designed such that the response system can be globally exponentially synchronized with the drive system. By utilizing a new lemma on impulsive differential inequality and the Lyapunov functional method, several synchronization criteria are obtained through rigorous mathematical proofs. Results of this paper are universal and can be applied to continuous chaotic systems. Moreover, numerical examples including discontinuous chaotic Chen system, memristor-based Chua’s circuit, and neural networks with discontinuous activations are given to verify the effectiveness of the theoretical results. Application of the obtained results to secure communication is also demonstrated in this paper.