On Stability of Discrete-Time Delay-Difference Equations for Arbitrary Delay Variations

Nikola Stankovic 1, 2 Sorin Olaru 3, 1 Silviu-Iulian Niculescu 3, 4
3 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
4 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
Abstract : This paper focuses on the concept of delay-independent stability for dynamical systems described by continuous linear delay-difference equations and the corresponding stability notion in discrete-time domain. The problem will be formulated with respect to delay-parameter space. Our intention is to summarize delay-independent stability condition and to provide, in a compact formulation, an appropriate numerical method for its computation, at least for two dimensional delay case. The obtained results are applied to the stability analysis of the discrete-time delay-difference equations. Such a strong stability condition appears to be necessary for the existence of specific invariant regions in the state-space. Some illustrative examples complete the paper.
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Submitted on : Monday, February 25, 2013 - 4:35:55 PM
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Nikola Stankovic, Sorin Olaru, Silviu-Iulian Niculescu. On Stability of Discrete-Time Delay-Difference Equations for Arbitrary Delay Variations. 11th Workshop on Time-Delay Systems, Feb 2013, Grenoble, France. pp.242-247, ⟨10.3182/20130204-3-FR-4031.00218⟩. ⟨hal-00794366⟩



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