Exponential stability of linear discrete systems with variable delays via Lyapunov Second method
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Date
2017-11-24
Authors
DiblĂk, Josef
ORCID
0000-0001-5009-316XAdvisor
Referee
Mark
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Hindawi
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Abstract
The paper investigates the exponential stability of a linear system of difference equations with variable delays. New criteria for exponential stability are derived using the method of Lyapunov functions and formulated in terms of the norms of matrices of linear terms and matrices solving an auxiliary Lyapunov equation. An exponential-type estimate of the norm of solutions is given as well. The efficiency of the derived criteria is numerically demonstrated by examples and their relations to the well-known results are discussed.
V ÄŤlánku je studována exponenciálnĂ stabilita lineárnĂch systĂ©mĹŻ diferenÄŤnĂch rovnic s promÄ›nnĂ˝mi zpoĹľdÄ›nĂmi. PomocĂ metody LjapunovovskĂ˝ch funkcĂ jsou odvozena nová kriteria exponenciálnĂ stability, která jsou formulována pomocĂ podmĂnek na normy matic a pomocĂ matic, která jsou Ĺ™ešenĂm pomocnĂ© Ljapunovovy rovnice. Dále jsou odvozeny expomenciálnĂ odhady norem Ĺ™ešenĂ. Efektivita kriterĂĂ je ilustrována na pĹ™Ăkladech a takĂ© jsou diskutovány souvislosti se znĂ˝mĂ˝mi vysledky.
V ÄŤlánku je studována exponenciálnĂ stabilita lineárnĂch systĂ©mĹŻ diferenÄŤnĂch rovnic s promÄ›nnĂ˝mi zpoĹľdÄ›nĂmi. PomocĂ metody LjapunovovskĂ˝ch funkcĂ jsou odvozena nová kriteria exponenciálnĂ stability, která jsou formulována pomocĂ podmĂnek na normy matic a pomocĂ matic, která jsou Ĺ™ešenĂm pomocnĂ© Ljapunovovy rovnice. Dále jsou odvozeny expomenciálnĂ odhady norem Ĺ™ešenĂ. Efektivita kriterĂĂ je ilustrována na pĹ™Ăkladech a takĂ© jsou diskutovány souvislosti se znĂ˝mĂ˝mi vysledky.
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DISCRETE DYNAMICS IN NATURE AND SOCIETY. 2017, vol. 2017, issue 1, p. 1-9.
https://www.hindawi.com/journals/ddns/2017/7417909/
https://www.hindawi.com/journals/ddns/2017/7417909/
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Peer-reviewed
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en