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Robust state‐feedback stabilization of jump linear systems via LMIs
Author(s) -
El Ghaoui Laurent,
Rami Mustapha Ait
Publication year - 1996
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/(sici)1099-1239(199611)6:9/10<1015::aid-rnc266>3.0.co;2-0
Subject(s) - control theory (sociology) , bounded function , mathematics , state (computer science) , constant (computer programming) , jump , stability (learning theory) , moment (physics) , stochastic matrix , linear system , matrix (chemical analysis) , control (management) , computer science , markov chain , mathematical analysis , physics , algorithm , statistics , materials science , quantum mechanics , classical mechanics , artificial intelligence , machine learning , composite material , programming language
We consider a linear system subject to Markovian jumps, with a time‐varying, unknown‐but‐bounded transition probability matrix. We derive LMI conditions ensuring various second‐moment stability properties for the system. The approach is then used to generate mode‐dependent state‐feedback control laws which stabilize the system in the mean‐square sense. When the transition probability matrix is constant and known, our conditions are necessary and sufficient.