{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T10:18:09Z","timestamp":1773656289504,"version":"3.50.1"},"reference-count":19,"publisher":"Pleiades Publishing Ltd","issue":"7","license":[{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2017,7,1]],"date-time":"2017-07-01T00:00:00Z","timestamp":1498867200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Autom Remote Control"],"published-print":{"date-parts":[[2017,7]]},"DOI":"10.1134\/s0005117917070050","type":"journal-article","created":{"date-parts":[[2017,7,18]],"date-time":"2017-07-18T06:14:48Z","timestamp":1500358488000},"page":"1234-1242","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Stability and synchronization of oscillators: New Lyapunov functions"],"prefix":"10.1134","volume":"78","author":[{"given":"B. T.","family":"Polyak","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ya. I.","family":"Kvinto","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"137","published-online":{"date-parts":[[2017,7,19]]},"reference":[{"issue":"1","key":"655_CR1","first-page":"1","volume":"2","author":"F. Tricomi","year":"1933","unstructured":"Tricomi, F., Integrazione di un\u2019Equazione Differenziale Presentatasi in Electrotecnica, Annali della Scuola Normale Superiore di Pisa\u2014Classe di Scienze 2, 1933, Ser. 2, no. 1, pp. 1\u201320.","journal-title":"Annali della Scuola Normale Superiore di Pisa\u2014Classe di Scienze 2"},{"key":"655_CR2","volume-title":"Qualitative Theorie nichtlinearer Differentialgleichungen","author":"R. Reissig","year":"1963","unstructured":"Reissig, R., Sansone, G., and Conti, R., Qualitative Theorie nichtlinearer Differentialgleichungen (Qualitative Theory of Nonlinear Differential Equations), Edizioni Cremonese: Rome, 1963. Translated under the title Kachestvennaya teoriya nelineinykh differentsial\u2019nykh uravnenii, Moscow: Nauka, 1974."},{"key":"655_CR3","volume-title":"Theory of Oscillations","author":"A.A. Andronov","year":"1966","unstructured":"Andronov, A.A., Vitt, A.A., and Khaikin, S.E., Theory of Oscillations, Osford: Pergamon, 1966."},{"key":"655_CR4","volume-title":"Ustoichivost\u2019 nelineinykh sistem s needinstvennym polozheniem ravnovesiya","author":"A.Kh. Gelig","year":"1978","unstructured":"Gelig, A.Kh., Leonov, G.A., and Yakubovich, V.A., Ustoichivost\u2019 nelineinykh sistem s needinstvennym polozheniem ravnovesiya (Stability of Nonlinear Systems with Nonunique Equilibrium Position), Moskow: Nauka, 1978."},{"key":"655_CR5","volume-title":"Vvedenie v teoriyu upravleniya","author":"G.A. Leonov","year":"2004","unstructured":"Leonov, G.A., Vvedenie v teoriyu upravleniya (Control Theory. An Introduction), St. Petersburg: S.-Peterburg. Gos. Univ., 2004."},{"issue":"9","key":"655_CR6","doi-asserted-by":"publisher","first-page":"1557","DOI":"10.1134\/S0005117916090046","volume":"77","author":"B.T. Polyak","year":"2016","unstructured":"Polyak, B.T., Kuznetsov, O.N., and Chumachenko, V.V., Stability Study of a Power System with Unipolar Electromagnetic Brake, Autom. Remote Control, 2016, vol. 77, no. 9, pp. 1557\u20131566.","journal-title":"Autom. Remote Control"},{"key":"655_CR7","volume-title":"Teoriya ustoichivosti dvizheniya","author":"I.G. Malkin","year":"1966","unstructured":"Malkin, I.G., Teoriya ustoichivosti dvizheniya (Theory of Stability of Motion), Moscow: Nauka, 1966, 2nd ed."},{"key":"655_CR8","first-page":"33","volume-title":"Zadachi analiza i sinteza nelineinykh kolebatel\u2019nykh sistem","author":"A.G. Leonov","year":"1999","unstructured":"Leonov, A.G. and Smirnova, V.B., Samosinkhronizatsiya dvukh neuravnoveshennykh rotorov, nakhodyashchikhsya na absolyutno zhestkoi platforme s odnoi stepen\u2019yu svobody (Self-synchronization of Two Unbalanced Rotors on a Rigid Platform with One Degree of Freedom), in Zadachi analiza i sinteza nelineinykh kolebatel\u2019nykh sistem (Analysis and Synthesis of Nonlinear Oscillatory Systems), Preprint 146, St. Petersburg: IPMASH RAN, 1999, pp. 33\u201342."},{"key":"655_CR9","volume-title":"Synchronization in Science and Technology","author":"I.I. Blekhman","year":"1988","unstructured":"Blekhman, I.I., Synchronization in Science and Technology, New York: ASME Press, 1988."},{"key":"655_CR10","volume-title":"Sistemy fazovoi sinkhronizatsii v analogovoi i tsifrovoi sistemotekhnike","author":"G.A. Leonov","year":"2002","unstructured":"Leonov, G.A. and Seledgy, S.M., Sistemy fazovoi sinkhronizatsii v analogovoi i tsifrovoi sistemotekhnike (Phase Locked Loops in Array Processors), St. Petersburg: Nevskii Dialekt, 2002."},{"issue":"7","key":"655_CR11","doi-asserted-by":"publisher","first-page":"1248","DOI":"10.1134\/S0005117916070110","volume":"77","author":"A.V. Proskurnikov","year":"2016","unstructured":"Proskurnikov, A.V. and Parsegov, S.E., Problem of Uniform Deployment on a Line Segment for Second- Order Agents, Autom. Remote Control, 2016, vol. 77, no. 7, pp. 1248\u20131258.","journal-title":"Autom. Remote Control"},{"issue":"1","key":"655_CR12","doi-asserted-by":"publisher","first-page":"32","DOI":"10.1016\/j.physd.2010.08.004","volume":"240","author":"Y.P. Choi","year":"2011","unstructured":"Choi, Y.P., Ha, S.Y., and Yun, S.B., Complete Synchronization of Kuramoto Oscillators with Finite Inertia, Phys. D: Nonlin. Phenom., 2011, vol. 240, no. 1, pp. 32\u201344.","journal-title":"Phys. D: Nonlin. Phenom."},{"issue":"6","key":"655_CR13","doi-asserted-by":"publisher","first-page":"1539","DOI":"10.1016\/j.automatica.2014.04.012","volume":"50","author":"F. D\u00f6rfler","year":"2014","unstructured":"D\u00f6rfler, F. and Bullo, F., Synchronization in Complex Networks of Phase Oscillators: A Survey, Automatica, 2014, vol. 50, no. 6, pp. 1539\u20131564.","journal-title":"Automatica"},{"key":"655_CR14","unstructured":"Problemy setevogo upravleniya (Problems of Networked Control), Fradkov, A.L., Ed., Moscow\u2013Izhevsk: IKI, 2015."},{"key":"655_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-1635-0","volume-title":"Energy Function Analysis for Power System Stability","author":"M.A. Pai","year":"1989","unstructured":"Pai, M.A., Energy Function Analysis for Power System Stability, Boston: Kluwer, 1989."},{"key":"655_CR16","volume-title":"Power System Dynamics: Stability and Control","author":"J. Machowski","year":"2011","unstructured":"Machowski, J., Bialek, J., and Bumby, J., Power System Dynamics: Stability and Control, Hoboken: Wiley, 2011."},{"issue":"2","key":"655_CR17","doi-asserted-by":"publisher","first-page":"1269","DOI":"10.1109\/TPWRS.2015.2425885","volume":"31","author":"T.L. Vu","year":"2016","unstructured":"Vu, T.L. and Turitsyn, K., Lyapunov Functions Family Approach to Transient Stability Assessment, IEEE Trans. Power Syst., 2016, vol. 31, no. 2, pp. 1269\u20131277.","journal-title":"IEEE Trans. Power Syst."},{"key":"655_CR18","volume-title":"Dinamicheskie sistemy s tsilindricheskim fazovym prostranstvom","author":"E.A. Barbashin","year":"1969","unstructured":"Barbashin, E.A. and Tabueva, V.A., Dinamicheskie sistemy s tsilindricheskim fazovym prostranstvom (Dynamical Systems with Cylindrical Phase Space), Moscow: Nauka, 1969."},{"issue":"3","key":"655_CR19","doi-asserted-by":"publisher","first-page":"877","DOI":"10.1142\/S0218127408020732","volume":"18","author":"G.A. Leonov","year":"2008","unstructured":"Leonov, G.A., Hilbert\u2019s 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation, Int. J. Bifurcat. Chaos, 2008, vol. 18, no. 3, pp. 877\u2013884.","journal-title":"Int. J. Bifurcat. Chaos"}],"container-title":["Automation and Remote Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117917070050.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1134\/S0005117917070050","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1134\/S0005117917070050.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T22:26:04Z","timestamp":1773613564000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1134\/S0005117917070050"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,7]]},"references-count":19,"journal-issue":{"issue":"7","published-print":{"date-parts":[[2017,7]]}},"alternative-id":["655"],"URL":"https:\/\/doi.org\/10.1134\/s0005117917070050","relation":{},"ISSN":["0005-1179","1608-3032"],"issn-type":[{"value":"0005-1179","type":"print"},{"value":"1608-3032","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,7]]},"assertion":[{"value":"9 November 2016","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 July 2017","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}