{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,9]],"date-time":"2025-05-09T14:51:20Z","timestamp":1746802280100,"version":"3.40.5"},"reference-count":12,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100014435","name":"Cardinal Stefan Wyszy\u0144ski University in Warsaw","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100014435","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The problem of<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>th mean exponential stability and stabilizability of a class of stochastic nonlinear and bilinear hybrid systems with unstable and stable subsystems is considered. Sufficient conditions for the<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>th mean exponential stability and stabilizability under a feedback control and stabilizing switching rules are derived. A method for the construction of stabilizing switching rules based on the Lyapunov technique and the knowledge of regions of decreasing the Lyapunov functions for subsystems is given. Two cases, including single Lyapunov function and a a single Lyapunov-like function, are discussed. Obtained results are illustrated by examples.<\/jats:p>","DOI":"10.1155\/2013\/206190","type":"journal-article","created":{"date-parts":[[2013,3,18]],"date-time":"2013-03-18T17:03:35Z","timestamp":1363626215000},"page":"1-10","source":"Crossref","is-referenced-by-count":2,"title":["<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>-Stability and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>p<\/mml:mi><\/mml:mrow><\/mml:math>-Stabilizability of Stochastic Nonlinear and Bilinear Hybrid Systems under Stabilizing Switching Rules"],"prefix":"10.1155","volume":"2013","author":[{"given":"Ewelina","family":"Seroka","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszy\u0144ski University in Warsaw, Dewajtis Street 5, 01-815 Warsaw, Poland"}]},{"given":"Les\u0142aw","family":"Socha","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Natural Sciences, College of Sciences, Cardinal Stefan Wyszy\u0144ski University in Warsaw, Dewajtis Street 5, 01-815 Warsaw, Poland"}]}],"member":"311","reference":[{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0017-8"},{"key":"8","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1109\/37.793443","volume":"19","year":"1999","journal-title":"IEEE Control Systems Magazine"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.nahs.2009.07.005"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1080\/0020717021000023762"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1016\/j.sysconle.2005.04.005"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1080\/00207720010015690"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2008.2012009"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012900370788"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1080\/07362999408809364"},{"year":"2004","key":"15"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2011.06.006"},{"year":"1997","key":"10"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/206190.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/206190.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/206190.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,6]],"date-time":"2020-05-06T04:26:42Z","timestamp":1588739202000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/206190\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":12,"alternative-id":["206190","206190"],"URL":"https:\/\/doi.org\/10.1155\/2013\/206190","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}