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

V. Z. Tsalyuk

Chair of Computational Mathematics and Information Science, Kuban State University, Krasnodar, Russia

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.

Keywords: functional differential inclusion, Cauchy function, exponential stability, multivalued delay.

UDC: 517.929

Received: 22.12.2008

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 36–48

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