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Parameterized LMIs for robust H 2 and H ∞ state feedback control of continuous‐time polytopic systems
Author(s) -
Rodrigues L.A.,
Oliveira R.C.L.F.,
Camino J.F.
Publication year - 2017
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.3911
Subject(s) - parameterized complexity , bounded function , scalar (mathematics) , control theory (sociology) , lemma (botany) , mathematics , linear matrix inequality , robustness (evolution) , domain (mathematical analysis) , robust control , linear system , mathematical optimization , computer science , control system , control (management) , mathematical analysis , algorithm , engineering , ecology , biochemistry , chemistry , geometry , poaceae , artificial intelligence , gene , electrical engineering , biology
Summary This paper presents new extended linear matrix inequality (LMI) characterizations for the synthesis of robust H ∞ and H 2 state feedback controllers for continuous‐time linear time‐invariant systems with polytopic uncertainty. Based on a suitable change of variables and the Elimination Lemma, the proposed robust control design techniques are stated as extended LMI conditions parameterized in terms of 2 scalar parameters. One parameter is shown to belong to a bounded domain, thus limiting the scalar search domain. For the other parameter, a bounded subset is provided from numerical experiments. The benefits of the methodology are illustrated through numerical simulations performed on an uncertain model borrowed from the literature. It is shown that the proposed LMI relaxations can provide less conservative results with fewer scalar searches than some existing methods in the literature.