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Stability of linear functional differential systems with a multivalued feedback with respect to impulse disturbances

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Abstract

We consider a linear controlled functional differential system with a linear feedback channel. The system is assumed to be exponentially stable in the closed state. The feedback is assumed to be nonideal, which consists in an uncertain delay either distributed or not. The only assumption is that this delay is sufficiently small. Such a nonideal system is described by a functional differential inclusion of special type. A generalized derivative of a function of locally bounded variation is admitted to the input of the system as a free term. We obtain exponential estimates for solutions of the resulting system.

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Authors and Affiliations

  1. Kuban State University, ul. Stavropol’skaya 149, Krasnodar, 350040, Russia

    V. Z. Tsalyukmail

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  1. V. Z. Tsalyukmail
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Correspondence to V. Z. Tsalyukmail.

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Original Russian Text © V.Z. Tsalyuk, 2010, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, No. 9, pp. 43–56.

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Tsalyukmail, V.Z. Stability of linear functional differential systems with a multivalued feedback with respect to impulse disturbances. Russ Math. 54, 36–48 (2010). https://doi.org/10.3103/S1066369X10090045

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  • DOI: https://doi.org/10.3103/S1066369X10090045

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