Delay-range-dependent ℋ^∞ synchronization approaches for time-delay chaotic systems

Abstract

The purpose of this paper is to investigate the problem of ${\mathcal{H}}^{\mathrm{\infty }}$ controller design for synchronization of the chaotic drive and response systems accompanied with bounded time delays limited by delay rates, uncertain parameters and admissible destabilization. An adequate condition is obtained employing the linear matrix inequality and a neoteric Lyapunov–Krasovskii functional to guarantee the global exponential synchronization of the studied chaotic systems. A control law is applied which would be added to the studied systems such that we can ensure the synchronization of the objective systems. The approach is proposed to solve the problem of the asymptotic ${\mathcal{H}}^{\mathrm{\infty }}$ synchronization of the studied systems. Numerical examples are illustrated to prove the feasibility and effectiveness of the current approach in this paper.

Keywords:

• ${\mathcal{H}}^{\mathrm{\infty }}$ control
• synchronization
• chaotic system
• linear matrix inequality

2010 Mathematics Subject Classification:

• 34H10

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grant 11705122, Science and Technology Program of Sichuan under Grant 2020YFH0124, and Zigong Key Science and Technology Project of China under Grant 2020YGJC01.

Disclosure statement

No potential conflict of interest was reported by the author(s).