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Avtomatika i Telemekhanika, 2021, Issue 1, Pages 83–94
DOI: https://doi.org/10.31857/S0005231021010049 (Mi at15472) 		 
Nonlinear Systems

A criterion for the asymptotic stability of a periodic selector-linear differential inclusion

M. V. Morozov

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117997 Russia
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DOI: https://doi.org/10.31857/S0005231021010049
Abstract: We consider a periodic selector-linear differential inclusion. It is proved that for this inclusion to be uniformly asymptotically stable, it is necessary and sufficient that there exists a time-periodic Lyapunov function of a quasi-quadratic form. We derive estimates for the Lyapunov function that guarantee its positive definiteness and the existence of an infinitesimal upper limit.
Keywords: periodic selector-linear differential inclusion, Lyapunov function.
Presented by the member of Editorial Board: L. B. Rapoport

Received: 19.05.2020
Revised: 07.07.2020
Accepted: 09.07.2020
English version:
Automation and Remote Control, 2021, Volume 82, Issue 1, Pages 63–72
DOI: https://doi.org/10.1134/S0005117921010045
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. V. Morozov, “A criterion for the asymptotic stability of a periodic selector-linear differential inclusion”, Avtomat. i Telemekh., 2021, no. 1, 83–94; Autom. Remote Control, 82:1 (2021), 63–72
Citation in format AMSBIB
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