This article is cited in 3 papers

Positive invertibility of matrices and exponential stability of impulsive systems of Ito linear differential equations with bounded delays

R. I. Kadiev^ab, A. V. Ponosov<sup>c

a</sup> Daghestan Scientific Centre of Russian Academy of Sciences, M. Gadjieva str., 45, Makhachkala, 367032 Russia
^b Dagestan State University, 43 a Hajiyev str., Makhachkala, 367025, Russia
^c Norwegian University of Life Sciences, P.O. Box 5003 N-1432, As, Norway

Abstract: Based on the theory of inverse-positive matrices, some problems of exponential $2p$–stability $(1 \le p < \infty )$ of systems of linear differential Ito equations with bounded delays and impulse effects on the part of the solution components are investigated. The ideas and methods developed by N.V. Azbelev and his students to study deterministic stability of functional dfferential equations are applied. For the above mentioned systems of equations, suffcient conditions for exponential $2p$-stability ($(1 \le p < \infty )$ are given in terms of positive invertibility of matrices constructed via the parameters of these systems. Feasibility of these conditions is checked for speciffic systems of equations.

Keywords: Ito equations, stability of solutions, impulse effects, positive invertibility of matrices, bounded delays.

UDC: 517.929:519.21

Received: 30.07.2019
Revised: 30.07.2019
Accepted: 18.12.2019

DOI: 10.26907/0021-3446-2020-8-18-35

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:8, 14–29

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