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Guaranteed cost control of uncertain discrete‐time singular Markov jump systems with indefinite quadratic cost
Author(s) -
Ma Shuping,
Boukas ElKébir
Publication year - 2011
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.1640
Subject(s) - discrete time and continuous time , mathematics , weighting , upper and lower bounds , quadratic equation , control theory (sociology) , markov chain , mathematical optimization , jump , matrix (chemical analysis) , bellman equation , state (computer science) , markov process , control (management) , computer science , algorithm , mathematical analysis , statistics , medicine , physics , geometry , materials science , quantum mechanics , artificial intelligence , composite material , radiology
The guaranteed cost control problem for discrete‐time singular Markov jump systems with parameter uncertainties is discussed. The weighting matrix in quadratic cost function is indefinite. For full and partial knowledge of transition probabilities cases, state feedback controllers are designed based on linear matrix inequalities method which guarantee that the closed‐loop discrete‐time singular Markov jump systems are regular, causal and robust stochastically stable, and the cost value has a zero lower bound and a finite upper bound. A numerical example to illustrate the effectiveness of the method is given in the paper. Copyright © 2010 John Wiley & Sons, Ltd.