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ℒ︁ 2 ‐Stabilization of continuous‐time linear systems with saturating actuators
Author(s) -
Castelan E. B.,
Tarbouriech S.,
Gomes da Silva J. M.,
Queinnec I.
Publication year - 2006
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.1118
Subject(s) - control theory (sociology) , linear matrix inequality , lyapunov function , actuator , lemma (botany) , mathematics , nonlinear system , stability (learning theory) , bounded function , quadratic equation , state (computer science) , linear system , mathematical optimization , control (management) , computer science , mathematical analysis , ecology , physics , geometry , poaceae , algorithm , quantum mechanics , artificial intelligence , machine learning , biology
This paper addresses the problem of controlling a linear system subject to actuator saturations and to ℒ 2 ‐bounded disturbances. Linear matrix inequality (LMI) conditions are proposed to design a state feedback gain in order to satisfy the closed‐loop input‐to‐state stability (ISS) and the closed‐loop finite gain ℒ 2 stability. By considering a quadratic candidate Lyapunov function, two particular tools are used to derive the LMI conditions: a modified sector condition , which encompasses the classical sector‐nonlinearity condition considered in some previous works, and Finsler ' s Lemma , which allows to derive stabilization conditions which are adapted to treat multiple objective control optimization problems in a potentially less conservative framework. Copyright © 2006 John Wiley & Sons, Ltd.
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