An example of nonlinear discrete-time synchronization of chaotic systems for secure communication

Belmouhoub, I.; Djemaï, M.; Barbot, Jean Pierre

doi:10.23919/ecc.2003.7086580

Cited by 4 publications

(3 citation statements)

References 19 publications

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“…In most works, synchronization is achieved asymptotically. It has been demonstrated in the case of non-linear integer-order discrete-time systems that synchronization can be immediate and accurate thanks to the use of an exact state reconstructor or a dead beat observer (Belmouhoub et al, 2003;Sira-Ramirez and Rouchon, 2001;Sira-Ramirez et al, 2002). In addition, the immediate recovery of encrypted information is a real challenge.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune

Bettayeb

Al‐Saggaf

2019

International Journal of Applied Mathematics and Computer Science

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This paper deals with the synchronization of fractional-order chaotic discrete-time systems. First, some new concepts regarding the output-memory observability of non-linear fractional-order discrete-time systems are developed. A rank criterion for output-memory observability is derived. Second, a dead-beat observer which recovers exactly the true state system from the knowledge of a finite number of delayed inputs and delayed outputs is proposed. The case of the presence of an unknown input is also studied. Third, secure data communication based on a generalized fractional-order Hénon map is proposed. Numerical simulations and application to secure speech communication are presented to show the efficiency of the proposed approach.

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Section: Introductionmentioning

confidence: 99%

Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Djennoune

Bettayeb

Al‐Saggaf

2019

International Journal of Applied Mathematics and Computer Science

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“…Let us notice that one of the attractive and efficient synchronization techniques, largely investigated during the last decade, is based on state observers design [1]- [2]- [3]- [4]- [5]- [6]. If continuoustime nonlinear systems benefit from a well developed control theory, analysis and synthesis of discrete-time systems remain a complex and difficult problem in particular state observers design as can be shown in [7]- [8].…”

Section: Introductionmentioning

confidence: 99%

Input recovery for a class of nonlinear multimodel system: An LMI approach

Hua

Boutayeb

Bara

et al. 2008

2008 16th Mediterranean Conference on Control and Automation

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In this note, we investigate the problem of state observation and input recovery of a particular class of nonlinear systems based on multi-models with unknown input. For this particular system and a corresponding observer structure, an original set of sufficient LMI conditions are derived from the Lyapunov theory, allowing to compute the gains of the observers and assuring asymptotic convergence. A numerical example is given in the context of secure communication, showing the practical interest of the method.Index Terms-Unknown input observer, Discrete-time multimodel system, Lipschitz nonlinear system, linear matrix inequalities.

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“…Such a problem (LInP), is motivated by the fact that usually, in a control scheme, u is on the left side and y is on the right side of the block diagram. If (1) is invertible with respect to the unknown input u, the construction of a delayed observer like in [5] allows us to completely recover the information u. Such a delayed observer was implemented as a deciphering process for a secure communication application.…”

Section: Problem Statement and Quadratic Equivalencementioning

confidence: 99%

Discrete-time Normal Form for Left Invertibility Problem

Djemaï

Barbot

Belmouhoub

2009

European Journal of Control

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This paper deals with the design of quadratic and higher order normal forms for the left invertibility problem. The linearly observable case and one-dimensional linearly unobservable case are investigated. The interest of such a study in the design of a delayed discrete-time observer is examined. The example of the Burgers map with unknown input is treated and a delayed discrete-time observer is designed. Finally, some simulated results are commented.

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An example of nonlinear discrete-time synchronization of chaotic systems for secure communication

Cited by 4 publications

References 19 publications

Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Synchronization of fractional–order discrete–time chaotic systems by an exact delayed state reconstructor: Application to secure communication

Input recovery for a class of nonlinear multimodel system: An LMI approach

Discrete-time Normal Form for Left Invertibility Problem

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