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Stochastic stability and guaranteed cost control of discrete‐time uncertain systems with Markovian jumping parameters
Author(s) -
Boukas ElKébir,
Shi Peng
Publication year - 1998
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(1998110)8:13<1155::aid-rnc380>3.0.co;2-f
Subject(s) - parametric statistics , mathematics , control theory (sociology) , bounded function , discrete time and continuous time , robust control , algebraic number , norm (philosophy) , quadratic equation , stability (learning theory) , mathematical optimization , control (management) , computer science , control system , mathematical analysis , statistics , geometry , artificial intelligence , machine learning , law , political science , electrical engineering , engineering
Abstract In this paper, we first study the problems of robust quadratic mean‐square stability and stabilization for a class of uncertain discrete‐time linear systems with both Markovian jumping parameters and Frobenius norm‐bounded parametric uncertainities. Necessary and sufficient conditions for the above problems are proposed, which are in terms of positive‐definite solutions of a set of coupled algebraic Riccati inequalities. Then, the problem of robust quadratic guaranteed cost control for the underlying systems is investigated. A guaranteed cost control is designed to ensure the cost function is within a certain bound, irrespective of all admissible uncertainities. © 1998 John Wiley & Sons, Ltd.