A New Synchronization Principle for a Class of Lur'e Systems with Applications in Secure Communication

In this Letter, we propose a new synchronization principle for a class of Lur'e systems. We design, using only a single scalar output, a possible class of observers to detect whether two dynamical systems exhibit identical oscillations. The proposed method is then applied to suggest a means to secure communications. The transmitter contains a chaotic oscillator with an input that is modulated by the information signal. The receiver is a copy of the transmitter driven by a synchronization signal. The advantage of this method over the existing one is that the synchronization time is explicitly computed. An illustrative example of the cubic Chua's circuit is given to show the effectiveness of the proposed approach.

[1]  E. Solak,et al.  On the Synchronization of Chaos Systems by Using State Observers , 1997 .

[2]  Ned J. Corron,et al.  A new approach to communications using chaotic signals , 1997 .

[3]  L. Chua,et al.  Communication Systems via Chaotic Signals from a Reconstruction Viewpoint , 1997 .

[4]  S. Mascolo,et al.  Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal , 1997 .

[5]  Henk Nijmeijer,et al.  An observer looks at synchronization , 1997 .

[6]  Maciej Ogorzalek,et al.  Taming chaos. I. Synchronization , 1993 .

[7]  H. Leung,et al.  Design of demodulator for the chaotic modulation communication system , 1997 .

[8]  Teh-Lu Liao,et al.  An observer-based approach for chaotic synchronization with applications to secure communications , 1999 .

[9]  Leon O. Chua,et al.  Experimental Demonstration of Secure Communications via Chaotic Synchronization , 1992, Chua's Circuit.

[10]  Kestutis Pyragas SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS , 1998 .

[11]  Michael Peter Kennedy Chaos in the Colpitts oscillator , 1994 .

[12]  Leon O. Chua,et al.  Spread Spectrum Communication Through Modulation of Chaos , 1993 .

[13]  Alan V. Oppenheim,et al.  Synchronization of Lorenz-based chaotic circuits with applications to communications , 1993 .

[14]  N J Corron Loss of synchronization in coupled oscillators with ubiquitous local stability. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Henk Nijmeijer,et al.  An observer for phase synchronization of chaos , 2001 .

[16]  R. Rajamani,et al.  Observer design for nonlinear systems: stability and convergence , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[17]  Ilse Cervantes,et al.  Stability of Observer-Based Chaotic Communications for a Class of Lur'e Systems , 2002, Int. J. Bifurc. Chaos.

[18]  Louis M. Pecora,et al.  Synchronizing chaotic circuits , 1991 .

[19]  T. Hartley The Duffing Double Scroll , 1989, 1989 American Control Conference.

[20]  Morgül,et al.  Observer based synchronization of chaotic systems. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[21]  Xiao-Song Yang On Observability of 3D Continuous-Time Autonomous Chaotic Systems Based on Scalar Output Measurement , 2002, Int. J. Bifurc. Chaos.

[22]  V. I. Korobov A GENERAL APPROACH TO THE SOLUTION OF THE BOUNDED CONTROL SYNTHESIS PROBLEM IN A CONTROLLABILITY PROBLEM , 1980 .

[23]  Leon O. Chua,et al.  Transmission of Digital signals by Chaotic Synchronization , 1992, Chua's Circuit.

[24]  Rabinder N Madan,et al.  Chua's Circuit: A Paradigm for Chaos , 1993, Chua's Circuit.

[25]  Kevin M. Short,et al.  Steps Toward Unmasking Secure Communications , 1994 .