{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T01:23:19Z","timestamp":1768353799785,"version":"3.49.0"},"reference-count":25,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2020,3,16]],"date-time":"2020-03-16T00:00:00Z","timestamp":1584316800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"funder":[{"DOI":"10.13039\/501100004742","name":"National Academy of Sciences of Ukraine","doi-asserted-by":"publisher","award":["6541230"],"award-info":[{"award-number":["6541230"]}],"id":[{"id":"10.13039\/501100004742","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,3,16]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The paper deals with the problem of stabilizing the equilibrium states of a family of non-linear non-autonomous systems. It is assumed that the nominal system is a linear controlled system with periodic coefficients. For the nominal controlled system, a new method for constructing a Lyapunov function in the quadratic form with a variable matrix is proposed. This matrix is defined as an approximate solution of the Lyapunov matrix differential equation in the form of a piecewise exponential function based on partial sums of a W. Magnus series. A stabilizing control in the form of a linear feedback with a piecewise constant periodic matrix is constructed. This control simultaneously stabilizes the considered family of systems. The estimates of the domain of attraction of an asymptotically stable equilibrium state of a closed-loop system that are common for all systems are obtained. A numerical example is given.<\/jats:p>","DOI":"10.1093\/imamci\/dnaa003","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T12:10:13Z","timestamp":1580472613000},"page":"125-142","source":"Crossref","is-referenced-by-count":3,"title":["Robust stabilization of non-linear non-autonomous control systems with periodic linear approximation"],"prefix":"10.1093","volume":"38","author":[{"given":"V I","family":"Slyn\u2019ko","sequence":"first","affiliation":[{"name":"Institute of Mathematics, University of W\u00fcrzburg, Emil-Fischer-Stra\u00dfe 40, 97074 W\u00fcrzburg, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cemil","family":"Tun\u00e7","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, 65080-Campus, Van, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"V O","family":"Bivziuk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Illinois at Urbana-Champaign, Champaign, IL, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2020,3,16]]},"reference":[{"key":"2021021910075759200_ref1","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1016\/j.sysconle.2011.11.016","article-title":"On robust Lie-algebraic stability conditions for switched linear systems","volume":"61","author":"Agrachev","year":"2012","journal-title":"Syst. 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