Further remarks on asymptotic stability and set invariance for linear delay-difference equations

Nikola Stanković 1 Sorin Olaru 2, 1 Silviu-Iulian Niculescu 3
2 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
Abstract : We studied the existence of positively invariant sets for linear delay-difference equations. In particular, we regarded two strong stability notions: robust (with respect to delay parameter) asymptotic stability for the discrete-time case and delay-independent stability for the continuous-time case. The correlation between these stability concepts is also considered. Furthermore, for the delay-difference equations with two delay parameters, we provided a computationally efficient numerical routine which is necessary to guarantee the existence of contractive sets of Lyapunov–Razumikhin type. This condition also appears to be necessary and sufficient for the delay-independent stability and sufficient for the robust asymptotic stability.
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Automatica, Elsevier, 2014, 50 (8), pp.2191-2195. 〈10.1016/j.automatica.2014.05.019〉
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Soumis le : mardi 16 décembre 2014 - 15:23:33
Dernière modification le : jeudi 5 avril 2018 - 12:30:13

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Nikola Stanković, Sorin Olaru, Silviu-Iulian Niculescu. Further remarks on asymptotic stability and set invariance for linear delay-difference equations. Automatica, Elsevier, 2014, 50 (8), pp.2191-2195. 〈10.1016/j.automatica.2014.05.019〉. 〈hal-01095962〉

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