Observer-Based Synchronization of Chaotic Systems Satisfying Incremental Quadratic Constraints and Its Application in Secure Communication

This paper presents a secure chaotic communication scheme using observer-based synchronization of chaotic systems. A class of chaotic systems satisfying incremental quadratic constraints are considered as the transmitter. The original message is encrypted in the noise-like output of the system. A circle criterion-based observer is designed for the system as the receiver by using the linear matrix inequalities technique. The message is recovered at the receiver end from the estimation error of the observer. To design the observer, a general algorithm to calculate incremental multiplier matrices for nonlinearities in chaotic systems is presented. Moreover, the proposed observer-based chaotic secure communication scheme is feasible for many common chaotic systems with ellipsoidal bounds. The simulation results show the good performance of the proposed communication scheme through an example of image transmission.

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