Synchronization Control Design Based On Observers For Time-delay Lur’e Systems

Jing Zhang,Shuzhen Huo,Zhanshan Zhao,Qi Cui

doi:10.1109/access.2020.2995082

Abstract

This paper researches synchronization control design for chaotic Lur'e systems (CLSs) with time-varying delay. Considering of the unmeasurable state variables, Luenberger-type observers are designed for the master-slave systems. The synchronization has been achieved by using the proposed controller with the estimated system states. Based on Bessel-Legendre inequality, improved reciprocally convex combination approach and a novel double integral inequality, new Lyapunov Krasovskii functionals(LKFs) are tailored and a synchronization control criterion with less conservatism is obtained. Some simulations are given to verify that this control strategy we proposed is effective.

Highlights

As is well known, chaos synchronization is a hot topic in recent years and receives much attention for the reason of its wide applicability in many scientific areas such as neural network [1]–[5], biomedical [6] and spacecraft [7]
Chaos synchronization could be seen as a special case of chaos control
Theorem 1: For given scalars nd = 1, dm, dM, hN based on the observers(3)(4) and employing feedback controller(5), with positive definite matrices Pi, Zi(i = 1, 2, 3), Xl(l = 1, . . . , 6), Qm(m = 1, . . . , 9), Qm = diag{Qm, 3Qm, 5Qm}, Wi, Qi = diag{qi}, Gi = diag{gi} and arbitrary matrices Ni with appropriate dimensions, the state estimation error systems(6)(7) and the synchronization error system (8) are asymptotically stable if:

Summary

Introduction

Chaos synchronization is a hot topic in recent years and receives much attention for the reason of its wide applicability in many scientific areas such as neural network [1]–[5], biomedical [6] and spacecraft [7]. Chaos demonstrates the oscillatory behavior which is unavoidable in dynamic nonlinear systems and shows a great sensitivity to initial conditions. A great deal of control methods have been developed to restrain chaos [8], [9]. Chaos synchronization could be seen as a special case of chaos control. The driving-response synchronization is by employing control strategies to make the response system gradually synchronize to the driving system. In the past few decades, a variety of approaches for chaos synchronization have been proposed. Adaptive control [1], [10], sliding mode control [11], adaptive fuzzy control [12]

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Conclusion