1 SYNCHRONIZATION OF 4-D HYPERCHAOTIC QI SYSTEM BY HIGH GAIN OBSERVER Souad Najoua Lagmiri 1 , El Houssine El Mazoudi 2 , Noureddine Elalami 1 1 Laboratoire d’Automatique et Informatique Industrielle, Ecole Mohammedia d’Ingénieurs Avenue Ibn Sina 765, Agdal Rabat, MAROC. najoua.lagmiri@gmail.com. elalami@emi.ac.ma. 2 Laboratoire de recherche en Economie de l’Energie, Environnement ET Ressources, Département d’Economie University Caddy Ayyad, Marrakech, MAROC. h_mazoudi@yahoo.fr ABSTRACT. This paper investigates the master-slave synchronization of two identical 4-D hyperchaotic Qi systems via a nonlinear high gain observer. Our aim is to implement the chaos synchronization via a nonlinear observer which synchronizes a slave hyperchaotic Qi system to a master system. The synchronization via high gain observer consists of leading the slave trajectories to the master system trajectories. Our purpose is to illustrate that the error between the real and the estimated system tends to zero when the observer gains growth. The verification is simulated with Matlab. INTRODUCTION In the last few years, several researchers have focused their attention on the problems related to the synchronization of chaotic systems [1]-[7]. Since chaos is characterized by a sensitive dependence on initial conditions. One can conclude that synchronization is not obtainable, because even infinitesimal change will eventually result in divergence of nearby starting orbits [l]. In order to overcome this drawback, different methods have been proposed [l]-[3]. However, most of the developed methods are concerned with the synchronization of low dimensional systems that is characterized by only one positive Lyapunov Exponent (LE). Since this feature limits the complexity of the chaotic dynamics, the adoption of higher dimensional chaotic systems has been proposed [4]. In general, hyperchaos with more than one positive Lyapnov Exponent (LE) is more disordered than ordinary chaos. Hyperchaotic systems have more complicated topological structures and dynamics than ordinary chaotic ones [6]. Furthermore, hyperchaos has attracted more attention to applications such as synchronization and communication encryption [2]. In most of the chaos synchronization approaches, the master-slave or drive-response formalism has been used. If a particular chaotic system is called the master or drive system and another chaotic system is called the slave or response system, then the idea of synchronization is to use the output of the master system to control the slave system so that the output of the slave system tracks the output of the master system asymptotically. [5] This paper is organized as follows. In Section 2, we define our 4-D hyperchaotic Qi system. In Section 3, we expose the high gain observer that we used to synchronize our hyperchotic system. In Section 4, we derive results for the master-slave synchronization of 4-D hyperchaotic Qi system. Conclusions are contained in the final section. KEYWORDS Nonlinear Control, Synchronization, Hyperchaos, Hyperchaotic Qi System, high gain observer.