Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

Abstract

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization (ATVMPS) of different dimensional chaotic systems (DDCSs) with time delays and unknown parameters. Firstly, to estimate the unknown parameters, adaptive parameter updated laws are designed. Secondly, to realize the fixed-time ATVMPS of the time-delayed DDCSs, an adaptive delay-unrelated controller is designed, where time delays of chaotic systems are known or unknown. Thirdly, some simple fixed-time ATVMPS criteria are deduced, and the rigorous proof is provided by employing the inequality technique and Lyapunov theory. Furthermore, the settling time of fixed-time synchronization (Fix-TS) is obtained, which depends only on controller parameters and system parameters and is independent of the system’s initial states. Finally, simulation examples are presented to validate the theoretical analysis.