Robust nonlinear H/sub ∞/ synchronization of chaotic Lur'e systems

2009

Nonlinear Analysis: Real World Applications, 2007

In this work we present a thorough investigation of the effect of noise (internal or external) on the synchronization of a driveresponse configuration system (unidirectional coupling between two identical systems). Moreover, since in every practical implementation of a communication system, the transmitter and receiver circuits (although identical) operate under slightly different conditions it is essential to consider the case of the mismatch between the parameters of the transmitter and the receiver. In our work we consider the non-autonomous second order non-linear oscillator system presented by G. Mycolaitis et al. in Proceedings of Seventh International Workshop on Nonlinear Dynamics of Electronic Systems [Globally synchronizable non-autonomous chaotic oscillator, Denmark, July 1999, pp. 277-280], which is particularly suitable for digital communications. Binary information is encoded by combining square pulses of two different frequencies selected so that the system is always in the chaotic regime independent of the encoded message. ᭧

Communications in Nonlinear Science and Numerical Simulation, 2012

In this paper we deal with the synchronization and parameter estimations of an uncertain Rikitake system and its application in secure communications employing chaotic parameter modulation. The strategy consists of proposing a receiver system which tends to follow asymptotically the unknown Rikitake system, refereed as transmitter system. The gains of the receiver system are adjusted continually according to a convenient high order slidingmode adaptative controller (HOSMAC), until the measurable output errors converge to zero. By using HOSMAC, synchronization between transmitter and receiver is achieved and message signals are recovered. The convergence analysis is carried out by using Barbalat's Lemma.

2006

In this paper, synchronization of two chaotic signals is studied and analyzed. A nonlinear recursive backstepping scheme is utilized to design an appropriate control input signal that achieves synchronization between the two chaotic signals. For the sake of comparison, an alternative master-slave synchronizing controller is designed and the two controllers are compared. Numerical simulations are used to demonstrate the effectiveness of the designed control signals in synchronizing the two chaotic systems. The study demonstrates a promising technique which can be applied in secure communication applications, whereby a chaoticallytransmitted information-bearing signal can be faithfully recovered via synchronization.

The University of Danang - Journal of Science and Technology, 2022

Chaos theory is one of the fields of research that has many practical applications. An important application of chaos in communication is that it can be used for secure communication. To be able to use the chaotic signal in communication, we need to synchronize the chaotic signal between the receiver and the transmitter. In this paper, a sliding mode controller is proposed for global synchronization between two chaotic systems. The interesting point of this controller is that it can help reduce the synchronization time based on the selection of the appropriate gain parameter. This method has also been applied to a secure communication system with chaos masking. Finally, numerical simulations are given to illustrate the effectiveness of the proposed method.

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1997

In this letter we introduce a new master-slave synchronization scheme for Lur'e systems, which makes use of vector field modulation and dynamic output feedback in order to recover a message signal. The synchronization scheme is represented in standard plant form according to modern control theory. I/O properties of the scheme are analyzed using a dissipativity approach with a quadratic storage function and a supply rate with finite L 2 -gain. The method avoids transmission of the full state vector. The controller design is based on a matrix inequality, corresponding to nonlinear H 1 synchronization. The new scheme is illustrated on Chua's circuit. Index Terms-Chua's circuit, dissipativity, dynamic output feedback, L 2 -gain, Lur'e systems, master-slave synchronization, matrix inequality, nonlinear H1 control. L. O. Chua is with the

Fifth World Congress on Intelligent Control and Automation (IEEE Cat. No.04EX788)

In this paper, we study the synchronization of three chaotic T-system with known and unknown parameters. The nonlinear feedback control and adaptive control schemes are used for synchronization with known and unknown parameters respectively. In unknown parameter case, each of systems has two unknown parameters and one known parameter. The stability of synchronization of three system is proved using Lyapunov stability theorem. Also, we use the synchronization of three chaotic systems with unknown parameters in secure communication via masking method. In secure communication, known parameters, unknown parameters, an affine combination of states, and coefficients are used for encryption and decryption. Numerical simulations are shown the effectiveness and feasibility of presented method.

Understanding Complex Systems, 2011

International Journal of Bifurcation and Chaos, 2005

In this article, the secure transmission of data is being realized on the basis of the synchronization of two chaotic systems. The transmitted signal is only the sign of a projection of the state. This has the advantage of making the transmission not very sensitive to the noises of transmission and the attenuation of the transmitted signal without using a VCO (Voltage Control Oscillatory) into the transmitter and the receiver. It should be noted that for the considered type of chaotic system, the traditional conditions of observability and linearization by injection of outputs are not checked. Here, we can only carry out an estimator.

2008