On the stability of solutions of nonlinear systems with impulse structure

N. I. Zhelonkina^ab, A. N. Sesekin<sup>ba

a</sup> Ural Federal University
^b N.N. Krasovskii Institute of Mathematics and Mechanics UB RAS

Abstract: In this paper we review the results of the authors related to the study of the stability property of solutions for nonlinear systems of differential equations, on the right-hand side of which there are terms containing products of discontinuous functions and distributions. The solutions of such systems are formalized by the closure of the set of smooth solutions in the space of functions of bounded variation. For such systems, sufficient conditions are obtained for the asymptotic stability of unperturbed solutions.

Keywords: nonlinear systems, impulse action, stability, asymptotic stability.

UDC: 517.911

Received: 13.04.2018

DOI: 10.20310/1810-0198-2018-23-124-624-636

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