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Rational representations and robust stabilization in the behavioral framework
Author(s) -
Gottimukkala Sasanka V.,
Trentelman Harry L.
Publication year - 2014
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3257
Subject(s) - control theory (sociology) , representation (politics) , controller (irrigation) , contrast (vision) , differential (mechanical device) , computer science , work (physics) , robust control , mathematical optimization , mathematics , control (management) , artificial intelligence , control system , engineering , mechanical engineering , agronomy , electrical engineering , politics , political science , law , biology , aerospace engineering
Summary In this paper, we study the problem of robust stabilization for linear differential systems in the behavioral framework. We study the existence of controllers that regularly stabilize all plants in a given neighborhood around a certain nominal plant. We call such controllers robustly stabilizing controllers . This problem was studied in the behavioral framework by Trentelman, H.L et al . In contrast to their work, however, in the present paper, we study the problem considering neighborhoods that are defined entirely representation free. These neighborhoods are induced by different kinds of concepts of distance between behaviors. As one of our main results we obtain that a given controller regularly stabilizes all plants in one of these neighborhoods if and only if it regularly stabilizes all plants in all of the other neighborhoods. Copyright © 2014 John Wiley & Sons, Ltd.