ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs
Identifieur interne : 008706 ( Main/Exploration ); précédent : 008705; suivant : 008707ℒ︁2‐Gain analysis and control of uncertain nonlinear systems with bounded disturbance inputs
Auteurs : D. F. Coutinho [Brésil] ; M. Fu [Australie] ; A. Trofino [Brésil] ; P. Danès [France]Source :
- International Journal of Robust and Nonlinear Control [ 1049-8923 ] ; 2008-01-10.
Descripteurs français
- Wicri :
- topic : Droit d'auteur, Industrie électrotechnique.
English descriptors
- KwdEn :
- Annihilator, Appropriate dimensions, Automatic control, Conservativeness, Constant matrices, Control matrices, Convex, Convex characterization, Convex optimization, Copyright, Coutinho, Dissipation inequality, Disturbance input, Disturbance signals, Dynamical systems, Electrical engineering, Gain analysis, Ieee, Ieee conference, Ieee transactions, Inequality, International journal, John wiley sons, Linear matrix inequalities, Linear matrix inequality methods, Linear systems, Lmis, Lyapunov, Lyapunov function, Lyapunov function candidate, Lyapunov functions, Lyapunov stability, Matrix, Matrix function, Nonlinear, Nonlinear control, Nonlinear system, Nonlinear systems, Numerical examples, Optimization, Optimization problem, Other words, Output feedback controller, Parameterized, Parametrization, Polynomial lyapunov functions, Polynomial systems, Positive scalars, Rational systems, Regional stability, Robust, Robust control, Robust nonlinear control, Schur complement, State vector, Supply function, System matrices, Uncertain nonlinear systems, Uncertain parameters, Xfmg.
- Teeft :
- Annihilator, Appropriate dimensions, Automatic control, Conservativeness, Constant matrices, Control matrices, Convex, Convex characterization, Convex optimization, Copyright, Coutinho, Dissipation inequality, Disturbance input, Disturbance signals, Dynamical systems, Electrical engineering, Gain analysis, Ieee, Ieee conference, Ieee transactions, Inequality, International journal, John wiley sons, Linear matrix inequalities, Linear matrix inequality methods, Linear systems, Lmis, Lyapunov, Lyapunov function, Lyapunov function candidate, Lyapunov functions, Lyapunov stability, Matrix, Matrix function, Nonlinear, Nonlinear control, Nonlinear system, Nonlinear systems, Numerical examples, Optimization, Optimization problem, Other words, Output feedback controller, Parameterized, Parametrization, Polynomial lyapunov functions, Polynomial systems, Positive scalars, Rational systems, Regional stability, Robust, Robust control, Robust nonlinear control, Schur complement, State vector, Supply function, System matrices, Uncertain nonlinear systems, Uncertain parameters, Xfmg.
Abstract
This paper proposes a convex approach to regional stability and ℒ︁2‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁2‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁2‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.
Url:
DOI: 10.1002/rnc.1207
Affiliations:
- Australie, Brésil, France
- Midi-Pyrénées, Occitanie (région administrative), Rio Grande do Sul, Santa Catarina
- Toulouse
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<front><div type="abstract" xml:lang="en">This paper proposes a convex approach to regional stability and ℒ︁2‐gain analysis and control synthesis for a class of nonlinear systems subject to bounded disturbance signals, where the system matrices are allowed to be rational functions of the state and uncertain parameters. To derive sufficient conditions for analysing input‐to‐output properties, we consider polynomial Lyapunov functions of the state and uncertain parameters (assumed to be bounded) and a differential‐algebraic representation of the nonlinear system. The analysis conditions are written in terms of linear matrix inequalities determining a bound on the ℒ︁2‐gain of the input‐to‐output operator for a class of (bounded) admissible disturbance signals. Through a suitable parametrization involving the Lyapunov and control matrices, we also propose a linear (full‐order) output feedback controller with a guaranteed bound on the ℒ︁2‐gain. Numerical examples are used to illustrate the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.</div>
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