A Hybrid Approach for the Estimation of Time-Varying Delays of Discrete-Time Systems

Abstract This paper addresses the problem of the estimation of unknown time-varying delays of discrete-time systems. The problem is reformulated as a mode detection for hybrid systems with a switching law depending on the unknown delay. Some existing data-based residual methods used for the estimation of the mode of switching linear discrete-time systems are briefly reviewed and presented in a unified way. Furthermore, it is shown that the usual existence conditions of some detectors can be relaxed. Next, results concerning the so-called discernibility property are particularized to the hybrid formulation of the estimation problem. Finally, it is shown that the issue is especially interesting in the context of chaotic secure communications both for information recovery and cryptanalysis purposes.

[1]  Magnus Egerstedt,et al.  ASYMPTOTIC OBSERVERS FOR DISCRETE-TIME SWITCHED LINEAR SYSTEMS , 2005 .

[2]  Jordi Garcia-Ojalvo,et al.  Synchronization and communication with chaotic laser systems , 2005 .

[3]  J. Daafouz,et al.  Equivalence between the Lyapunov-Krasovskii functionals approach for discrete delay systems and that of the stability conditions for switched systems , 2008 .

[4]  G. Nikolakopoulos,et al.  Multi-hopping Induced Gain Scheduling for Wireless Networked Controlled Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[5]  L. Larger,et al.  Nonlocal Nonlinear Electro-Optic Phase Dynamics Demonstrating 10 Gb/s Chaos Communications , 2010, IEEE Journal of Quantum Electronics.

[6]  Jamal Daafouz,et al.  Equivalence between the lyapunov-krasovskii functional approach for discrete delay systems and the stability conditions for switched systems , 2007 .

[7]  S. Bjorklund,et al.  A review of time-delay estimation techniques , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[8]  P. Colet,et al.  Synchronization of chaotic semiconductor lasers: application to encoded communications , 1996, IEEE Photonics Technology Letters.

[9]  M. Egerstedt,et al.  Pathwise observability and controllability are decidable , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[10]  Magnus Egerstedt,et al.  Observability of Switched Linear Systems , 2004, HSCC.

[11]  Driss Boutat,et al.  Secure Data Transmission Based on Multi-Input Multi-Output Delayed Chaotic System , 2008, Int. J. Bifurc. Chaos.

[12]  Anthony Tzes,et al.  Development and experimental verification of a mobile client-centric networked controlled system , 2003, 2003 European Control Conference (ECC).

[13]  Didier Maquin,et al.  Switching systems mode estimation using a model-based diagnosis method , 2007 .