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Preservation of properties in discrete‐time systems under substitutions
Author(s) -
FernándezAnaya Guillermo,
FloresGodoy JoséJob,
ÁlvarezRamírez José
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.114
Subject(s) - bounded function , mathematics , norm (philosophy) , discrete time and continuous time , stability (learning theory) , lemma (botany) , control theory (sociology) , pure mathematics , discrete mathematics , control (management) , computer science , mathematical analysis , artificial intelligence , ecology , statistics , poaceae , machine learning , political science , law , biology
For discrete‐time systems, using substitutions of the variable z by 1 functions, we give results on preservation of stability, stabilization, positive real (PR), strictly positive real (SPR), bounded real (BR), and strictly bounded real (SBR) functions, along with the ℋ ∞ ‐norm. These results can be interpreted in the sense of robust control or uniform systems. Based on these properties, we present results about preservation of the SPR Lemma and absolute stability for discrete‐time descriptor systems using linear matrix inequalities (LMIs) and substitutions. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society