{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T16:40:23Z","timestamp":1782405623576,"version":"3.54.5"},"reference-count":49,"publisher":"Emerald","issue":"3-4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015,12,17]]},"abstract":"<jats:p>This paper presents a comprehensive study of continuous-time Positive Markov Jump Linear Systems (PMJLS). A PMJLS can be seen as a dynamical system that switches within a finite set of linear timeinvariant subsystems according to a stochastic switching signal modeled as a Markov chain, and describes the time-evolution of nonnegative variables under nonnegative inputs. Contrary to the well-studied general class of Markov Jump Linear Systems (MJLS), positivity endows the model with peculiar properties. The paper collects some existing results together with original developments on the stability analysis of PMJLS and the study of their input-output properties. In particular, conditions for stability of PMJLS are discussed, mainly based on Linear Programming problems. Similar computational tools are derived to analyze performance measures, such as L1,L2 and L\u221e costs and the respective input-output induced gains. The second part of the paper is devoted to the class of Dual switching Positive Markov Jump Linear Systems (D-PMJLS), namely PMJLS affected by an additional switching variable which can be either an unknown disturbance or a control signal available to the designer for stabilization and performance optimization. We discuss several problems, including stability, performance analysis, stabilization via switching control, and optimization. Some application examples are introduced to motivate the interest in PMJLS and D-PMJLS.<\/jats:p>","DOI":"10.1561\/2600000006","type":"journal-article","created":{"date-parts":[[2015,12,17]],"date-time":"2015-12-17T09:40:22Z","timestamp":1450345222000},"page":"275-427","source":"Crossref","is-referenced-by-count":62,"title":["Positive Markov Jump Linear Systems"],"prefix":"10.1108","volume":"2","author":[{"given":"Paolo","family":"Bolzern","sequence":"first","affiliation":[{"name":"DEIB-Politecnico di Milano"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Patrizio","family":"Colaneri","sequence":"additional","affiliation":[{"name":"DEIB-Politecnico di Milano and IEIIT-CNR"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"140","published-online":{"date-parts":[[2015,12,17]]},"reference":[{"key":"2026033114030905200_ref001","article-title":"Hybrid positive systems subject to markovian switching","volume-title":"Proceedings of 3rd IFAC Conference on Analysis and Design of Hybrid Systems","author":"Ait Rami"},{"key":"2026033114030905200_ref002","doi-asserted-by":"crossref","first-page":"2865","DOI":"10.3934\/dcdsb.2014.19.2865","article-title":"Stability criteria for SIS epidemiological models under switching policies","volume":"19","author":"Ait Rami","year":"2014","journal-title":"Discrete and continuous dynamical series B"},{"key":"2026033114030905200_ref003","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4606-6","volume-title":"Set-Theoretic Methods in Control","author":"Blanchini","year":"2008"},{"key":"2026033114030905200_ref004","first-page":"1507","article-title":"A convexity result for the optimal control of a class of positive nonlinear systems","volume-title":"Proceedings of the 19th IFAC World Congress","author":"Blanchini"},{"key":"2026033114030905200_ref005","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1561\/2600000005","article-title":"Switched linear positive systems","volume":"2","author":"Blanchini","year":"2015","journal-title":"Foundations and Trends in Systems and Control"},{"key":"2026033114030905200_ref006","doi-asserted-by":"crossref","first-page":"983","DOI":"10.1016\/j.automatica.2006.02.007","article-title":"On almost sure stability of continuous-time Markov jump linear systems","volume":"42","author":"Bolzern","year":"2006","journal-title":"Automatica"},{"key":"2026033114030905200_ref007","doi-asserted-by":"crossref","first-page":"114","DOI":"10.3166\/ejc.14.114-123","article-title":"Almost sure stability of stochastic linear systems with ergodic parameters","volume":"14","author":"Bolzern","year":"2008","journal-title":"European Journal of Control"},{"key":"2026033114030905200_ref008","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1016\/j.automatica.2010.03.007","article-title":"Markov Jump Linear Systems with switching transition rates: mean square stability with dwell-time","volume":"46","author":"Bolzern","year":"2010","journal-title":"Automatica"},{"key":"2026033114030905200_ref009","doi-asserted-by":"crossref","first-page":"1181","DOI":"10.1016\/j.automatica.2014.02.016","article-title":"Stochastic stability of positive Markov jump linear systems","volume":"50","author":"Bolzern","year":"2014","journal-title":"Automatica"},{"key":"2026033114030905200_ref010","first-page":"2359","article-title":"Stabilization via switching of positive Markov jump linear systems","volume-title":"Proceedings of 53d IEEE Conference on Decision and Control","author":"Bolzern"},{"key":"2026033114030905200_ref011","article-title":"H1 co-design for discrete-time dual switching linear systems","volume-title":"2015 European Control Conference - 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