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

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.