Open AccessBounded real lemma for positive discrete systems
Author(s) -
Wang Cuihong
Publication year - 2013
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2012.0167
Subject(s) - bounded function , control theory (sociology) , lemma (botany) , mathematics , computer science , mathematical analysis , control (management) , artificial intelligence , ecology , poaceae , biology
The bounded real lemma for positive discrete time‐invariant systems is addressed in this study. The results about bounded real lemma for continuous time‐invariant systems are extended into discrete time‐invariant systems. Such systems are asymptotically stable and their H ∞ norm less than one is equivalent to that the corresponding linear matrix inequality admits a diagonal positive‐definite solution. The last example in this study illustrates the result does not hold for general discrete time‐invariant systems.