Asian Journal of Control, Vol. 15, No. 1, pp. 1 9, January 2013 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/asjc.341 SYNCHRONIZING CHAOTIC SYSTEMS WITH PARAMETRIC UNCERTAINTY VIA A NOVEL ADAPTIVE IMPULSIVE OBSERVER Moosa Ayati, Hamid Khaloozadeh, and Xinzhi Liu ABSTRACT This paper proposes a new class of observers, called adaptive impulsive observers. These observers are capable of estimating the states and unknown parameters of an uncertain system using the output of the system at discrete jump times only. Through a proposed theorem, the stability of the states estimation error system is proved and an upper bound on the maximum possible impulses (jumps) interval is given. Due to these advantages, the proposed adaptive impulsive observer is used in a chaotic systems synchro- nization scheme. The presented simulation results show the effectiveness of the proposed observer even when the coupling signal is scalar. Key Words: Adaptive impulsive observer, impulsive synchronization, impul- sive system, parametric uncertainty. I. INTRODUCTION Since synchronization phenomena are pervasive in nature, chaos synchronization has attracted consider- able attention from scientists and engineers over the past two decades. In biological systems, e.g. chaotic neuron networks [1], a large number of studies have sought to unveil the mechanisms of synchronization from both physiological [2] and computational [3] viewpoints. Other applications of chaos synchronization are in networks [4], synchronizing robot manipulators [5], etc. (interested readers are referred to [6]). One of the interesting uses of chaotic systems is in chaotic secure communication systems. After the seminal work of Manuscript received April 19, 2010; revised September 16, 2010; accepted October 28, 2010. Moosa Ayati (corresponding author, e-mail: Ayati@ dena.kntu.ac.ir) and Hamid Khaloozadeh (e-mail: H Khaloozadeh@kntu.ac.ir) are with the Faculty of Elec- trical and Computer Engineering, K. N. Toosi University of Technology, Tehran, Iran. Xinzhi Liu is with the Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada (e-mail: xzliu@uwaterloo.ca). This research is supported by the Iran Telecommunication Research Center. Pecora and Carroll [7], several methods have been employed to theoretically and experimentally synchro- nize chaotic systems, such as sliding mode controllers and observers [8], adaptive control methods ([9–11]), impulsive control methods [12, 13], etc. Chaotic communication systems [14] are commu- nication systems where the transmitter (or drive system) modulates the message with a functional of the trans- mitter states or parameters and sends the modulated signal on the communication channel. In the receiver (or response system), utilizing a well-developed synchro- nization algorithm, the received signal is demodulated and the message is extracted. Generally, a synchro- nization algorithm is a method that estimates the drive system states or parameters using one or several coupling signals or control inputs. Investigating different synchronization methods shows that impulsive synchronization has shown great efficiency in chaos communication applications as it maintains synchronization by rather small synchroniza- tion impulses. Other synchronization methods, called continuous synchronization methods, demand contin- uous synchronization signals. In impulsive synchro- nization, since the response system receives a sequence of synchronizing impulses at discrete time instants, the communication channel capacity will be reserved for 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society