Synchronization of Chaotic Systems Using Sampled Data Polynomial Controller

Abstract

This paper presents the synchronization of two chaotic systems, namely the drive and response chaotic systems, using sampleddata polynomial controllers. The sampleddata polynomial controller is employed to drive the system states of the response chaotic system to follow those of the drive chaotic system. Because of the zeroorderhold unit complicating the system dynamics by introducing discontinuity to the system, it makes the stability analysis difficult. However, the sampleddata polynomial controller can be readily implemented by a digital computer or microcontroller to lower the implementation cost and time. With the sumofsquares (SOS) approach, the system to be handled can be in the form of nonlinear statespace equations with the system matrix depending on system states. Based on the Lyapunov stability theory, SOSbased stability conditions are obtained to guarantee the system stability and realize the chaotic synchronization subject to an Hâˆ‍ performance function. The solution to the SOSbased stability conditions can be found numerically using the thirdparty Matlab toolbox SOSTOOLS. Simulation examples are given to illustrate the merits of the proposed sampleddata polynomial control approach for chaotic synchronization problems.