Chaos synchronization of the master-slave generalized Lorenz systems via linear state error feedback control

摘要

This paper provides a unified method for analyzing chaos synchronization ofthe generalized Lorenz systems. The considered synchronization scheme consistsof identical master and slave generalized Lorenz systems coupled by linearstate error variables. A sufficient synchronization criterion for a generallinear state error feedback controller is rigorously proven by means oflinearization and Lyapunov's direct methods. When a simple linear controller isused in the scheme, some easily implemented algebraic synchronizationconditions are derived based on the upper and lower bounds of the masterchaotic system. These criteria are further optimized to improve theirsharpness. The optimized criteria are then applied to four typical generalizedLorenz systems, i.e. the classical Lorenz system, the Chen system, the Lvsystem and a unified chaotic system, obtaining precise correspondingsynchronization conditions. The advantages of the new criteria are revealed byanalytically and numerically comparing their sharpness with that of the knowncriteria existing in the literature.