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Robust H ∞ control of norm bounded uncertain systems via Markovian approach
Author(s) -
Wang Guoliang,
Zhang Qingling,
Sreeram Victor
Publication year - 2011
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.254
Subject(s) - bounded function , lyapunov function , norm (philosophy) , control theory (sociology) , mathematics , lemma (botany) , mathematical optimization , robust control , computer science , control (management) , control system , engineering , artificial intelligence , law , nonlinear system , mathematical analysis , ecology , physics , poaceae , electrical engineering , quantum mechanics , political science , biology
This paper presents a new approach to analyze and synthesize linear uncertain systems with time‐varying norm bounded uncertainty. Firstly, the uncertainty set is classified into several different subsets according to the maximum singular value of uncertainty. Then, based on the proposed classification, the original uncertain system is transformed into a Markovian jump system. By an uncertainty‐dependent Lyapunov function, new version of bounded real lemma is developed and two sufficient conditions for designing uncertainty‐dependent controllers are established. Finally, numerical examples and simulations are used to demonstrate the utility of the given methods.Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society