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A necessary and sufficient condition of stochastic stability for PMJLSs is given which can be checked by solving linear programming feasibility problems due to the positivity property. A common co-positive Lyapunov function is constructed to solve the problem, and the equivalence among stochastic stability, 1-moment stability and exponential mean stability is proved afterwards. Considering the uncertain transition rates situation, PMJLSs with partially known transition rate matrix are investigated, and a necessary and sufficient condition for robust stochastic stability is proposed in linear programming form. Numerical examples are presented to show the effectiveness of the proposed results.<\/jats:p>","DOI":"10.1177\/0142331218755577","type":"journal-article","created":{"date-parts":[[2018,3,26]],"date-time":"2018-03-26T07:51:44Z","timestamp":1522050704000},"page":"2724-2731","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":8,"title":["Stochastic stability of positive Markov jump linear systems with completely\/partially known transition rates"],"prefix":"10.1177","volume":"40","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5582-6438","authenticated-orcid":false,"given":"Ying","family":"Chen","sequence":"first","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, Nanjing, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuming","family":"Bo","sequence":"additional","affiliation":[{"name":"School of Automation, Nanjing University of Science and Technology, 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