caa a22 4500 445868511 CHVBK 20180317145505.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00498-011-0064-9 doi (NATIONALLICENCE)springer-10.1007/s00498-011-0064-9 Quadratic costs and second moments of jump linear systems with general Markov chain [Elektronische Daten] [Eduardo Costa, Alessandro Vargas, João do Val] This paper presents an analytic, systematic approach to handle quadratic functionals associated with Markov jump linear systems with general jumping state. The Markov chain is finite state, but otherwise general, possibly reducible and periodic. We study how the second moment dynamics are affected by the additive noise and the asymptotic behaviour, either oscillatory or invariant, of the Markov chain. The paper comprises a series of evaluations that lead to a tight two-sided bound for quadratic cost functionals. A tight two-sided bound for the norm of the second moment of the system is also obtained. These bounds allow us to show that the long-run average cost is well defined for system that are stable in the mean square sense, in spite of the periodic behaviour of the chain and taking into consideration that it may not be unique, as it may depend on the initial distribution. We also address the important question of approximation of the long-run average cost via adherence of finite horizon costs. Springer-Verlag London Limited, 2011 Linear systems nationallicence Markov jump systems nationallicence Long-run average cost nationallicence Bounds for finite horizon cost nationallicence Costa Eduardo Universidade de São Paulo (USP), Depto. de Matemática Aplicada e Estatística, C.P. 668, 13560-970, São Carlos, SP, Brazil aut Vargas Alessandro Universidade Estadual de Campinas (UNICAMP), Fac. de Eng. Elétrica e de Computação, Depto. de Telemática, C.P. 6101, 13081-970, Campinas, SP, Brazil aut do Val João Universidade Estadual de Campinas (UNICAMP), Fac. de Eng. Elétrica e de Computação, Depto. de Telemática, C.P. 6101, 13081-970, Campinas, SP, Brazil aut Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 141-157 0932-4194 23:1-3<141 2011 23 498 https://doi.org/10.1007/s00498-011-0064-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00498-011-0064-9 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Costa Eduardo Universidade de São Paulo (USP), Depto. de Matemática Aplicada e Estatística, C.P. 668, 13560-970, São Carlos, SP, Brazil aut NATIONALLICENCE 700 1- Vargas Alessandro Universidade Estadual de Campinas (UNICAMP), Fac. de Eng. Elétrica e de Computação, Depto. de Telemática, C.P. 6101, 13081-970, Campinas, SP, Brazil aut NATIONALLICENCE 700 1- do Val João Universidade Estadual de Campinas (UNICAMP), Fac. de Eng. Elétrica e de Computação, Depto. de Telemática, C.P. 6101, 13081-970, Campinas, SP, Brazil aut NATIONALLICENCE 773 0- Mathematics of Control, Signals, and Systems Springer-Verlag 23/1-3(2011-12-01), 141-157 0932-4194 23:1-3<141 2011 23 498 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer