Master–Slave Synchronization of Fourth-Order Lü Chaotic Oscillators via Linear Output Feedback

Abstract—We solve the problem of master–slave synchroniza-tion of fourth-order Lü’s hyperchaotic systems via feedback con-trol. We use only one control input that enters in the slave system. We show that this simple feedback suffices to synchronize both systems exponentially fast. We provide a proof of stability and con-vergence (hence, that synchronization takes place) via Lyapunov’s second stability method. We provide some numeric simulations that illustrate our findings. Index Terms—Chaos, control, synchronization. I. INTRODUCTION AND PROBLEM FORMULATION SYNCHRONIZATION of dynamical systems is a multifacetsubject of research depending on the context. It may be hi-erarchy based (unidirectional), such as “master–slave ” synchro-nization in which, typically but not necessarily, two systems are synchronized in a way that the “slave ” system mimics the mo