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On stability and stabilizability of positive delay systems
Author(s) -
Wu Ligang,
Lam James,
Shu Zhan,
Du Baozhu
Publication year - 2009
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.99
Subject(s) - control theory (sociology) , stability theory , stability (learning theory) , mathematics , matrix (chemical analysis) , linear matrix inequality , control (management) , computer science , mathematical optimization , nonlinear system , physics , materials science , quantum mechanics , artificial intelligence , machine learning , composite material
The stabilization problem with positivity is investigated in this note for discrete‐time linear systems with time delay. A delay‐independent necessary and sufficient condition is proposed in terms of linear matrix inequalities (LMIs) for the existence of desired controllers that guarantee the closed‐loop system to be asymptotically stable and positive. In addition, the obtained result is further extended to more general case when the system matrices contain uncertain parameters, where a sufficient condition is obtained. The frequently used polytopic parameter uncertainty is taken into consideration. Since the conditions obtained are expressed as LMIs, which can be easily verified by using standard numerical software. A numerical example is provided to illustrate the proposed results. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society