{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,5]],"date-time":"2025-03-05T05:44:24Z","timestamp":1741153464712,"version":"3.38.0"},"reference-count":19,"publisher":"SAGE Publications","issue":"13","license":[{"start":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T00:00:00Z","timestamp":1683849600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Transactions of the Institute of Measurement and Control"],"published-print":{"date-parts":[[2024,9]]},"abstract":"<jats:p> This paper studies the stability of discrete-time time-varying stochastic systems with infinite Markov switching. First, the concepts of strongly exponentially stable in mean square and exponentially stable in mean square with conditions are introduced, and their equivalent conditions are given by operator theory and stochastic analysis. Second, we introduce the Lyapunov equation related to strongly exponentially stable in mean square. Third, as an application of the proposed Lyapunov stability criterion, the relationship between the internal stability and the [Formula: see text] input\u2013output state stability is derived for the infinite Markov jump system disturbed by finite-energy random disturbance. Finally, an example is given to verify its correctness and validity. <\/jats:p>","DOI":"10.1177\/01423312231163927","type":"journal-article","created":{"date-parts":[[2023,5,12]],"date-time":"2023-05-12T12:08:37Z","timestamp":1683893317000},"page":"2664-2673","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":0,"title":["Stability analysis of discrete-time time-varying stochastic systems with infinite Markov switching"],"prefix":"10.1177","volume":"46","author":[{"given":"Zhiyong","family":"Ye","sequence":"first","affiliation":[{"name":"School of Science, Chongqing University of Technology, Chongqing, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6994-5825","authenticated-orcid":false,"given":"Hongxia","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Science, Chongqing University of Technology, Chongqing, China"}]},{"given":"Fang","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Science, Chongqing University of Technology, Chongqing, China"}]},{"given":"Xin","family":"He","sequence":"additional","affiliation":[{"name":"School of Science, Chongqing University of Technology, Chongqing, China"}]},{"given":"Anjian","family":"Xu","sequence":"additional","affiliation":[{"name":"School of Science, Chongqing University of Technology, Chongqing, China"}]}],"member":"179","published-online":{"date-parts":[[2023,5,12]]},"reference":[{"key":"bibr1-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2927589"},{"key":"bibr2-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1007\/s00020-005-1371-7"},{"key":"bibr3-01423312231163927","doi-asserted-by":"publisher","DOI":"10.3166\/ejc.12.373-395"},{"key":"bibr4-01423312231163927","first-page":"131","volume":"53","author":"Dragan V","year":"2008","journal-title":"Revue Roumaine Des Mathematiques Pures Et Appliquees"},{"key":"bibr5-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4419-0630-4"},{"key":"bibr6-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2002.800674"},{"key":"bibr7-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012903434753"},{"key":"bibr8-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2511306"},{"key":"bibr9-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1109\/ACC.2015.7171987"},{"key":"bibr10-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1360\/SSI-2020-0162"},{"key":"bibr11-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1007\/s11424-020-8364-0"},{"key":"bibr12-01423312231163927","doi-asserted-by":"publisher","DOI":"10.3182\/20110828-6-IT-1002.02412"},{"key":"bibr13-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1142\/p473"},{"key":"bibr14-01423312231163927","doi-asserted-by":"publisher","DOI":"10.23919\/ChiCC.2018.8483675"},{"key":"bibr15-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1080\/10236198.2012.704369"},{"key":"bibr16-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1177\/0142331210371815"},{"key":"bibr17-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2013.2266751"},{"key":"bibr18-01423312231163927","doi-asserted-by":"publisher","DOI":"10.1177\/0142331218757859"},{"key":"bibr19-01423312231163927","first-page":"6","volume":"2016","author":"Zhou HY","year":"2016","journal-title":"Control Engineering of China"}],"container-title":["Transactions of the Institute of Measurement and Control"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312231163927","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/full-xml\/10.1177\/01423312231163927","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.1177\/01423312231163927","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,4]],"date-time":"2025-03-04T18:16:21Z","timestamp":1741112181000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.1177\/01423312231163927"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5,12]]},"references-count":19,"journal-issue":{"issue":"13","published-print":{"date-parts":[[2024,9]]}},"alternative-id":["10.1177\/01423312231163927"],"URL":"https:\/\/doi.org\/10.1177\/01423312231163927","relation":{},"ISSN":["0142-3312","1477-0369"],"issn-type":[{"type":"print","value":"0142-3312"},{"type":"electronic","value":"1477-0369"}],"subject":[],"published":{"date-parts":[[2023,5,12]]}}}