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Reliable controllable sets for constrained Markov‐Jump Linear Systems
Author(s) -
HernándezMejías Manuel A.,
Sala Antonio,
Ariño Carlos,
Querol Andrés
Publication year - 2015
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3394
Subject(s) - markov chain , mathematics , generalization , sequence (biology) , upper and lower bounds , reliability (semiconductor) , set (abstract data type) , jump , mathematical optimization , state (computer science) , markov process , computer science , algorithm , statistics , mathematical analysis , power (physics) , genetics , physics , quantum mechanics , biology , programming language
Summary Robust λ ‐contractive sets have been proposed in previous literature for uncertain polytopic linear systems. It is well known that, if initial state is inside such sets, it is guaranteed to converge to the origin. This work presents the generalization of such concepts to systems whose behaviour changes among different linear models with probability given by a Markov chain. We propose sequence‐dependent sets and associated controllers that can ensure a reliability bound when initial conditions are outside the maximal λ ‐contractive set. Such reliability bound will be understood as the probability of actually reaching the origin from a given initial condition without violating constraints. As initial conditions are further away from the origin, the likelihood of reaching the origin decreases. Copyright © 2015 John Wiley & Sons, Ltd.