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Optimal guaranteed cost for singular linear systems with random abrupt changes
Author(s) -
Boukas ElKébir
Publication year - 2010
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.908
Subject(s) - jump , piecewise , class (philosophy) , mathematics , piecewise linear function , impulse (physics) , control theory (sociology) , mathematical optimization , linear matrix inequality , controller (irrigation) , computer science , control (management) , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , agronomy , biology
This paper considers the class of continuous‐time singular linear Markovian jump systems with totally and partially known transition jump rates. The guaranteed cost control problem of this class of systems is tackled. New sufficient conditions for optimal guaranteed cost are developed. A design procedure for the guaranteed cost controller, which guarantees that the closed‐loop dynamics will be piecewise regular, impulse‐free and stochastically stable is proposed. It is shown that the addressed problem can be solved if the corresponding developed linear matrix inequalities (LMIs) with some constraints are feasible. A numerical example is employed to show the usefulness of the proposed results. Copyright © 2009 John Wiley & Sons, Ltd.