{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,19]],"date-time":"2025-12-19T09:47:48Z","timestamp":1766137668569,"version":"3.37.3"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"10","license":[{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T00:00:00Z","timestamp":1619136000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2021,10]]},"DOI":"10.1007\/s00034-021-01709-6","type":"journal-article","created":{"date-parts":[[2021,4,23]],"date-time":"2021-04-23T06:02:31Z","timestamp":1619157751000},"page":"4799-4832","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Commutativity of Sixth-Order Time-Varying Linear Systems"],"prefix":"10.1007","volume":"40","author":[{"given":"Salisu","family":"Ibrahim","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7220-0042","authenticated-orcid":false,"given":"Mehmet Emir","family":"Koksal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,4,23]]},"reference":[{"issue":"3","key":"1709_CR1","first-page":"650","volume":"26","author":"MR Ainbund","year":"1983","unstructured":"M.R. Ainbund, I.P. Maslenkov, Improving the characteristics of micro channel plates in cascade connection. Instrum. Exp. Tech. 26(3), 650\u2013652 (1983)","journal-title":"Instrum. Exp. Tech."},{"key":"1709_CR2","volume-title":"Ordinary Differential Equations with Applications","author":"C Chicone","year":"2006","unstructured":"C. Chicone, Ordinary Differential Equations with Applications, 2nd edn. (Springer, Berlin, 2006).","edition":"2"},{"issue":"3","key":"1709_CR3","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1137\/0610024","volume":"10","author":"I Gohberg","year":"1989","unstructured":"I. Gohberg, M.A. Kaashoekve, A.C.M. Ran, Partial role and zero displacement by cascade connection. SIAM J. Matrix Anal. Appl. 10(3), 316\u2013325 (1989)","journal-title":"SIAM J. Matrix Anal. Appl."},{"issue":"2","key":"1709_CR4","doi-asserted-by":"publisher","first-page":"162","DOI":"10.1109\/TCT.1968.1082798","volume":"15","author":"AGJ Holt","year":"1968","unstructured":"A.G.J. Holt, K.M. Reineck, Transfer function synthesis for a cascade connection network. IEEE Trans. Circuit Theory 15(2), 162\u2013163 (1968)","journal-title":"IEEE Trans. Circuit Theory"},{"issue":"3","key":"1709_CR5","doi-asserted-by":"publisher","first-page":"541","DOI":"10.1080\/00207178208932914","volume":"36","author":"M Koksal","year":"1982","unstructured":"M. Koksal, Commutativity of second order time-varying systems. Int. J. Control 36(3), 541\u2013544 (1982)","journal-title":"Int. J. Control"},{"key":"1709_CR6","unstructured":"M. Koksal, General commutativity conditions for time-varying systems, in 2nd National Congress of Electrical Engineers, vol. 2, no. 2 (1987a), pp. 566\u2013569."},{"key":"1709_CR7","unstructured":"M. Koksal, Effects of nonzero initial conditions on commutativity and those of commutativity on system sensitivity, in 2nd National Congress of Electrical Engineers vol. 2, no, 2 (1987b), pp. 570\u2013573."},{"key":"1709_CR8","unstructured":"M. Koksal, Effects of nonzero initial conditions on commutativity and those of commutativity on system sensitivity, in 2nd National Congress of Electrical Engineers vol. 2, no. 2 (1987c) pp. 570\u2013573."},{"key":"1709_CR9","first-page":"49","volume":"1A","author":"M Koksal","year":"1988","unstructured":"M. Koksal, Effects of nonzero initial conditions on the commutativity of linear time-varying systems. Int. Conf. Model. Simul. 1A, 49\u201355 (1988)","journal-title":"Int. Conf. Model. Simul."},{"key":"1709_CR10","unstructured":"M. Koksal, Commutativity of 4th order systems and Euler systems, in Symposium of Yildiz Technical University on the Role of Engineering on the Development of our Country (1988a), pp. 398\u2013408."},{"issue":"5","key":"1709_CR11","doi-asserted-by":"publisher","first-page":"1521","DOI":"10.1080\/00207178808906113","volume":"47","author":"M Koksal","year":"1988","unstructured":"M. Koksal, An exhaustive study on the commutativity of time-varying systems. Int. J. Control 47(5), 1521\u20131537 (1988)","journal-title":"Int. J. Control"},{"key":"1709_CR12","unstructured":"M. Koksal, Effects of commutativity on system's sensitivity, in 6th International Symposium on Networks, Systems and Signal Processing, (1989), pp. 61\u201362."},{"key":"1709_CR13","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1155\/2011\/678575","volume":"2011","author":"M Koksal","year":"2011","unstructured":"M. Koksal, M.E. Koksal, Commutativity of linear time-varying differential systems with non-zero initial conditions: A review and some new extensions. Math. Probl. Eng. 2011, 1\u201325 (2011)","journal-title":"Math. Probl. Eng."},{"key":"1709_CR14","unstructured":"M. Koksal, M.E. Koksal, Ard\u0131\u015f\u0131k Ba\u011fl\u0131 Zamanla De\u011fi\u015fen Do\u011frusal Ayr\u0131k-zaman Sistemlerinin S\u0131ra-de\u011fi\u015fim \u00d6zelli\u011fi, Turkish National Meeting on Automatics Control, (2013), pp. 1128\u20131131"},{"key":"1709_CR15","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1177\/0142331214532678","volume":"37","author":"M Koksal","year":"2015","unstructured":"M. Koksal, M.E. Koksal, Commutativity of cascade connected discrete time linear varying systems. Trans. Inst. Meas. Control. 37, 615\u2013622 (2015)","journal-title":"Trans. Inst. Meas. Control."},{"key":"1709_CR16","doi-asserted-by":"crossref","unstructured":"M.E. Koksal, Inverse Commutativity Conditions for Second-order Linear Time-Varying Systems. J. Math. (2017), pp. 1\u20136.","DOI":"10.1155\/2017\/3070236"},{"issue":"3","key":"1709_CR17","doi-asserted-by":"publisher","first-page":"696","DOI":"10.1177\/0142331218765615","volume":"41","author":"ME Koksal","year":"2019","unstructured":"M.E. Koksal, Commutativity of systems with their feedback conjugates. Trans. Inst. Meas. Control. 41(3), 696\u2013700 (2019)","journal-title":"Trans. Inst. Meas. Control."},{"issue":"3","key":"1709_CR18","first-page":"413","volume":"29","author":"ME Koksal","year":"2019","unstructured":"M.E. Koksal, Explicit commutativity conditions for second order linear time varying systems with non-zero initial conditions. Archiv. Control Sci. 29(3), 413\u2013432 (2019)","journal-title":"Archiv. Control Sci."},{"issue":"3","key":"1709_CR19","doi-asserted-by":"publisher","first-page":"1385","DOI":"10.1007\/s00034-018-0911-8","volume":"38","author":"ME Koksal","year":"2019","unstructured":"M.E. Koksal, Transitivity of commutativity for second-order linear time-varying analogue systems. Circuits Syst. Signal Process. 38(3), 1385\u20131395 (2019)","journal-title":"Circuits Syst. Signal Process."},{"issue":"16","key":"1709_CR20","doi-asserted-by":"publisher","first-page":"5274","DOI":"10.1002\/mma.5310","volume":"42","author":"ME Koksal","year":"2019","unstructured":"M.E. Koksal, Commutativity of first-order discrete-time linear time-varying systems. Math. Methods Appl. Sci. 42(16), 5274\u20135292 (2019)","journal-title":"Math. Methods Appl. Sci."},{"issue":"10","key":"1709_CR21","doi-asserted-by":"publisher","first-page":"4446","DOI":"10.1007\/s00034-019-01075-4","volume":"38","author":"MEA KoksalYakar","year":"2019","unstructured":"M.E.A. KoksalYakar, Decomposition of a third-order linear time-system into its second and first-order commutative pairs. Circuits Syst. Signal Process. 38(10), 4446\u20134464 (2019)","journal-title":"Circuits Syst. Signal Process."},{"key":"1709_CR22","doi-asserted-by":"publisher","first-page":"539","DOI":"10.1049\/el:19770388","volume":"18","author":"E Marshall","year":"1977","unstructured":"E. Marshall, Commutativity of time-varying systems. Electron. Lett. 18, 539\u2013540 (1977)","journal-title":"Electron. Lett."},{"issue":"2","key":"1709_CR23","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1016\/S0947-3580(96)70034-1","volume":"2","author":"BT Polyak","year":"1976","unstructured":"B.T. Polyak, A.N. Vishnyakov, Multiplying disks, robust stability of a cascade connection. Eur. J. Control. 2(2), 101\u2013111 (1976)","journal-title":"Eur. J. Control."},{"key":"1709_CR24","doi-asserted-by":"publisher","first-page":"1195","DOI":"10.1080\/00207178308933041","volume":"37","author":"SV Saleh","year":"1983","unstructured":"S.V. Saleh, Comments on commutativity of second-order time-varying systems. Int. J. Control 37, 1195\u20131195 (1983)","journal-title":"Int. J. Control"},{"issue":"1","key":"1709_CR25","first-page":"56","volume":"86","author":"J Walczak","year":"2010","unstructured":"J. Walczak, A. Piwowar, Cascade connection of a parametric sections and its properties. Przeglad Elektrotechniczny 86(1), 56\u201358 (2010)","journal-title":"Przeglad Elektrotechniczny"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-021-01709-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00034-021-01709-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-021-01709-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,8,27]],"date-time":"2021-08-27T09:23:23Z","timestamp":1630056203000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00034-021-01709-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,23]]},"references-count":25,"journal-issue":{"issue":"10","published-print":{"date-parts":[[2021,10]]}},"alternative-id":["1709"],"URL":"https:\/\/doi.org\/10.1007\/s00034-021-01709-6","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2021,4,23]]},"assertion":[{"value":"29 July 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 March 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 April 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}