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32 results on '"Geometric control for non-linear systems (CONGE)"'

1. On the Genericity of the Observability for Controlled Discrete-time Systems

Author

Ammar, Sabeur, Vivalda, Jean-Claude, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
observability, discrete-time systems, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], nonlinear systems, transversality theory
Abstract

In this paper, we prove that observability is a generic property for discrete-time systems with more outputs than inputs.

Published
2003

2. A Jurdjevic-Quinn type theorem for nonlinear systems

Author

Mohamed Bensoubaya, Abderrahman Iggidr, A. Ferfera, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, Variable structure control, Pure mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 010102 general mathematics, 02 engineering and technology, Nonlinear control, Feedback passivation, 01 natural sciences, Sliding mode control, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, Small-gain theorem, 020901 industrial engineering & automation, Control theory, Control system, Feedback linearization, 0101 mathematics, Mathematics
Abstract

International audience; We consider non-affine control systems for which we give a sufficient condition for smooth stabilization. This condition generalizes the well known Jurdjevic-Quinn (1978) result for affine control systems. The stabilizing feedback is explicitly computed

Published
2002
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3. Stabilisation d'une population halieutique

Author

Ouahbi, Abderrahim, Iggidr, Abderrahman, El Bagdouri, Mohamed, Laboratoire d'Automatique et d'Etude des Procédés, Université Cadi Ayyad [Marrakech] (UCA), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience

Published
2002

4. Backstepping with bounded feedbacks for systems not in feedback form

Author

Abderrahman Iggidr, Frédéric Mazenc, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, 0209 industrial biotechnology, Computer science, 010102 general mathematics, Nonlinear control, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Feedback form, 02 engineering and technology, Extension (predicate logic), 01 natural sciences, stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, Backstepping, Bounded function, Strict-feedback form, symbols, 0101 mathematics
Abstract

International audience; An extension of the backstepping approach is proposed. It allows to globally asymptotically stabilize by bounded feedbacks families of nonlinear control systems which are not in feedback form. Copyright (C) 2001 IFAC.

Published
2001

5. On the dynamic behavior of a hydraulic cylinder

Author

E. Richard, M. Haloua, Abderrahman Iggidr, Ecole Mohammadia d'Ingénieurs (EMI), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), Centre de Recherche en Automatique de Nancy (CRAN), Université Henri Poincaré - Nancy 1 (UHP)-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, Engineering, Feedback control, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], hydraulic cylinder, electrohydraulic control equipment, 01 natural sciences, Stability (probability), nonlinear control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Physics::Fluid Dynamics, valves, symbols.namesake, Control theory, 0101 mathematics, Hydraulic machinery, leakages, Lyapunov stability, business.industry, 010102 general mathematics, Linear system, servomechanisms, stability, 010101 applied mathematics, dynamic behavior, Hydraulic cylinder, stability properties, Nonlinear model, hydraulic systems, nonlinear model, symbols, business
Abstract

International audience; We are interested in the stability properties of a hydraulic cylinder when no control is applied. We give a nonlinear model that take into account the leakages and show that the system is Lyapunov stable

Published
2000

6. State estimation for a fish population via a nonlinear observer

Author

M. Oumoun, Jean-Claude Vivalda, Abderrahman Iggidr, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
age-structured model, 0209 industrial biotechnology, Observer (quantum physics), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], stock-recruitment function, 02 engineering and technology, 01 natural sciences, discrete time systems, nonlinear control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Control theory, nonlinear observer, exponential observer, population dynamics, Quantitative Biology::Populations and Evolution, 14. Life underwater, State observer, 0101 mathematics, natural resources, Population dynamics of fisheries, Mathematics, Estimation, observers, estimation, 010102 general mathematics, observer, Function (mathematics), State (functional analysis), difference equations, exploited fish population, Exponential function, non- linear control systems, Nonlinear system, discrete-time systems, fish population
Abstract

International audience; This paper focuses on the construction of an exponential observer for an age-structured model of an exploited fish population in order to get an estimation of the number of fishes by age class. The considered model is nonlinear and involves a stock-recruitment function which is not well known. The observer that we construct is independent of this function.

Published
2000
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7. A simple observer for nonlinear discrete-time systems, application to a population dynamics model

Author

Jean-Claude Vivalda, Abderrahman Iggidr, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine

Subjects
0209 industrial biotechnology, demography, Observer (quantum physics), Computer science, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Constructive, discrete time systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 03 medical and health sciences, 020901 industrial engineering & automation, Control theory, Simple (abstract algebra), dead-beat observer, population dynamics, State observer, education, state feedback, 030304 developmental biology, nonlinear discrete-time systems, 0303 health sciences, education.field_of_study, observers, difference equations, dynamics, Nonlinear system, Discrete time and continuous time, nonlinear systems
Abstract

International audience; A constructive dead-beat observer design method for nonlinear discrete systems is given and illustrated with an application to a model of population dynamics.

Published
2000
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8. On the regulation of the state of a harvested fish population

Author

Jean-Claude Vivalda, M. El Bagdouri, A. Ouahbi, Abderrahman Iggidr, Laboratoire d'Automatique et d'Etude des Procédés, Université Cadi Ayyad [Marrakech] (UCA), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, Engineering, Steady state (electronics), [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Quantitative Biology::Other, 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, 020901 industrial engineering & automation, Aquaculture, Control theory, Quantitative Biology::Populations and Evolution, 14. Life underwater, 0101 mathematics, natural resources, Population dynamics of fisheries, asymptotic stability, business.industry, 010102 general mathematics, Fishery, aquaculture, fish population, State (computer science), nonlinear systems, business, fishery model
Abstract

International audience; The goal of this paper is to apply some tools of control theory to an age-structured fishery model in order to stabilize an exploited fish population around a nontrivial steady state.

Published
2000
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9. Stabilization of nonlinear stochastic discrete systems

Author

Abderrahman Iggidr, Mohamed Bensoubaya, A. Ferfera, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, 0209 industrial biotechnology, sufficient condition, probability, stochastic systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Stability (learning theory), feedback, 02 engineering and technology, feedback stabilization, Nonlinear control, Type (model theory), 01 natural sciences, discrete time systems, nonlinear control systems, Algebraic Riccati equation, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, 0101 mathematics, Mathematics, Lyapunov functions, Stochastic control, 010102 general mathematics, stability, Nonlinear system, nonlinear stochastic discrete systems, stochastic stability, symbols, Nonlinear discrete systems, Stochastic optimization
Abstract

International audience; Our goal is to give a sufficient condition for feedback stabilization of nonlinear stochastic discrete systems. The stabilization problem of both continuous-time and discrete-time deterministic nonlinear control systems has attracted the interest of an increasing number of authors in the last decades and various techniques have been developed to design stabilizing feedback. As for stabilization of stochastic nonlinear control systems, only few results are available in the literature. Properties of the solution of the stochastic algebraic Riccati equation introduced by Wonham (1968) are used by Gao and Ahmed (1987) to deal with the stabilizability problem for a class of continuous-time stochastic nonlinear control systems. More recently, by using the Lyapunov functions method, a stochastic version of Artstein-Sontag's theorem is established in Chabour and Oumoun (1999), while a Jurdjevic-Quinn type theorem is stated in Bensoubaya et al. In this paper we give a sufficient condition for global stabilization of discrete-time stochastic systems. This condition is the discrete analogue of the Jurdjevic-Quinn type condition derived in Bensoubaya et al. for continuous-time stochastic control systems.

Published
1999
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10. On the Control of an Exploited Population of Fish

Author

Abderrahman Iggidr, A. Ouahbi, J. C. Vivaida, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire d'Automatique et d'Etude des Procédés, Université Cadi Ayyad [Marrakech] (UCA), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 020301 aerospace & aeronautics, 0209 industrial biotechnology, education.field_of_study, Feedback control, Population, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, difference equations, Feedback, stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, 0203 mechanical engineering, Exponential stability, Control theory, symbols, population dynamics, %22">Fish , 14. Life underwater, education, Control (linguistics), Lyapunov functions
Abstract

International audience; The aim of this paper is to show how some tools of control theory can be helpful to regulate the exploitation of a population of fish.

Published
1999
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11. Use of non linear software sensor to monitor the internal state of a culture of microalgae

Author

Gauthier Sallet, Olivier Bernard, Antoine Sciandra, Centre for systems engineering and applied mechanics [Louvain] (CESAME), Université Catholique de Louvain = Catholic University of Louvain (UCL), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire d'océanographie de Villefranche (LOV), Observatoire océanologique de Villefranche-sur-mer (OOVM), Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Institut national des sciences de l'Univers (INSU - CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, and Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0106 biological sciences, 0209 industrial biotechnology, High-gain antenna, Engineering, business.industry, Exponential convergence, Control engineering, 02 engineering and technology, Chemostat, 010603 evolutionary biology, 01 natural sciences, Nonlinear system, 020901 industrial engineering & automation, Software, [INFO.INFO-AU]Computer Science [cs]/Automatic Control Engineering, Bioreactor, Voltage droop, State (computer science), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], business, ComputingMilieux_MISCELLANEOUS
Abstract

We construct nonlinear software sensors in order to monitor the internal state of a culture of microalgae. We use the Droop model to represent the growth of phytoplanktonic cells limited by nutrients in the bioreactor. We show that this model is an element of a general class of systems for which the conditions for the exponential convergence of high gain observers are proved. The software sensors is then designed and applied in a nitrate-limited microalgae chemostat experiment performed in a computer controlled fluctuating environment. The efficiency of the software sensor is discussed.

Published
1999
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12. Stabilization of nonlinear systems by use of semidefinite Lyapunov functions

Author

Abderrahman Iggidr, Mohamed Bensoubaya, Abdelhak Ferfera, Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, Semidefinite functions, 0209 industrial biotechnology, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Lyapunov exponent, Positive-definite matrix, Nonlinear control, 01 natural sciences, Feedback, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, Nonlinear systems, Lyapunov equation, 0101 mathematics, Lyapunov redesign, ComputingMilieux_MISCELLANEOUS, Lyapunov functions, Mathematics, Applied Mathematics, 010102 general mathematics, Stabilization, Nonlinear system, Control system, symbols, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
Abstract

We give a sufficient condition for smooth stabilization of nonlinear control systems. This condition generalizes the well-known Jurdjevic-Quinn results in the sense that it uses nonnegative semidefinite Lyapunov functions rather than positive definite ones, and that it applies to nonaffine control systems. Stabilizing feedback is explicitly computed.

Published
1999
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13. Exponential Stability and Transfer Functions of a Heat Exchanger Network System

Author

Xu, Cheng-Zhong, Sallet, Gauthier, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
exponential stability, symmetric hyperbolic equations, heat exchangers, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], transfer functions, regular systems
Abstract

In this paper we study frequency and time domain behaviour of a heat exchanger network system. The system is governed by hyperbolic partial differential equations. Both the control operator and the observation operator are unbounded but admissible. Using the theory of symmetric hyperbolic systems, we prove exponential stability of the underlying semigroup for the heat exchanger network. Applying the recent representation theory of infinite-dimen- sional linear systems, we prove that the system is regular and derive various properties for the transfer functions, which are potentially useful for controller design.

Published
1999

14. Global stabilization of stochastic nonlinear systems

Author

A. Ferfera, Abderrahman Iggidr, Mohamed Bensoubaya, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, Pure mathematics, Differential equation, stochastic systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, Nonlinear control, 01 natural sciences, Omega, nonlinear control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Wiener process, Control theory, stochastic nonaffine nonlinear control systems, 0101 mathematics, state feedback, Mathematics, Stochastic process, stability criteria, 010102 general mathematics, global stabilization, deterministic affine control systems, bounded smooth state feedback, State (functional analysis), Nonlinear system, Bounded function, standard Wiener process, symbols
Abstract

International audience; We consider stochastic nonaffine nonlinear control systems dxt=f(xt,u) dt+g(xt,u) dωt, ω being a standard Wiener process, for which we give a sufficient condition for global stabilization by a bounded smooth state feedback which is explicitly given. This condition generalizes the well known Jurdjevic-Quinn result (1978) for deterministic affine control systems

Published
1998
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15. Global stabilization of planar homogeneous polynomial systems

Author

Rachid Outbib, Abderrahman Iggidr, H. Jghima, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, 0209 industrial biotechnology, Applied Mathematics, 010102 general mathematics, Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, 01 natural sciences, Matrix polynomial, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, Nonlinear system, 020901 industrial engineering & automation, Planar, Stable polynomial, Homogeneous polynomial, symbols, Applied mathematics, Kharitonov's theorem, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Analysis, ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

International audience

Published
1998
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16. Nonlinear Feedback Stabilization of a Rotating Body-Beam Without Damping

Author

Chentouf, Boumediène, Couchouron, Jean-François, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
exponential stability, rotating body-beam, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], nonlinear control
Abstract

This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping. The feedback law proposed hereother end. We assume that there is no damping. The feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a consists of a nonlinear control torque applied to the rigid body and either a nonlinear boundary control moment or a nonlinear boundary control force or both nonlinear boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls. This new class of controls is in particular of the interest to be robust.

Published
1998

17. Stabilization of periodic discrete-time nonlinear systems

Author

A. Ferfera, Abderrahman Iggidr, Mohamed Bensoubaya, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, 0209 industrial biotechnology, sufficient conditions, Computer science, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], periodic discrete systems, 02 engineering and technology, Stability (probability), discrete time systems, nonlinear control systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Discrete system, symbols.namesake, periodic discrete-time nonlinear systems, time-varying stabilizing control, 020901 industrial engineering & automation, Exponential stability, Control theory, 0202 electrical engineering, electronic engineering, information engineering, stabiliza- tion, Sampled data systems, asymptotic stability, time-varying feedback, 020208 electrical & electronic engineering, Time-invariant system, periodic control, stability, Discrete time nonlinear systems, time-varying systems, autonomous discrete systems, symbols, control system synthesis
Abstract

International audience; This paper provides sufficient conditions for stabilizing periodic discrete systems. These conditions are derived from a discrete version of a theorem due to Krasovski for continuous-time systems. This tool allows us to give a systematic design of time-varying stabilizing control for autonomous discrete systems that can not be stabilized by time-invariant feedback

Published
1997
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18. Global stabilization of nonaffine control systems

Author

Bensoubaya, Mohamed, Ferfera, Abdelhak, Iggidr, Abderrahman, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience

Published
1997

19. Stabilisation d'une équation de vibrations

Author

Chentouf, Boumediène, Xu, Cheng-Zhong, Sallet, Gauthier, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
contrôle non linéaire, multiplicateur, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], stabilité forte, semi-groupe de contractions non linéaire, principe d'invariance de Lasalle, stabilité exponentielle, système en boucle fermé
Abstract

Cet article traite la stabilisation frontière d'une équation de vibrations. On démontre que le système peut être stabilisé fortement ou exponentiellement par des feedbacks frontières non linéaires.

Published
1997

20. Stability of Discrete-time Systems : New Criteria and Applications to Control Problems

Author

Iggidr, Abderrahman, Bensoubaya, Mohamed, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
[INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], feedback, difference equations, stability, nonlinear control systems, semi-definite function
Abstract

The aim of this article is to present some new stability sufficient conditions for discrete-time nonlinear systems. It shows how to use nonnegative semi-definite functions as Lyapunov functions instead of positive definite ones for studying the stability of a given system. Several examples and some applications to control theory are presented to illustrate the various theorems.

Published
1996

21. Time-varying stabilizing feedback for a class of nonlinear discrete-time control systems

Author

A. Ferfera, Abderrahman Iggidr, M. Bensoabaza, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, time-varying stabilizing feedback, 0209 industrial biotechnology, Computer science, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], feedback, 02 engineering and technology, Sliding mode control, nonlinear control systems, discrete time systems, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Control theory, 0202 electrical engineering, electronic engineering, information engineering, Feedback linearization, Computer Science::Databases, Lyapunov functions, Linear system, Control engineering, stability, Feedback passivation, time-varying systems, nonautonomous systems, stabilization, nonlinear discrete-time control systems, Nonlinear system, Control system, symbols, 020201 artificial intelligence & image processing, State (computer science)
Abstract

International audience; The goal of this paper is to introduce and to use time-varying control for the stabilization of nonlinear discrete-time control systems which can not be stabilized by state feedback.

Published
1995
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22. Feedback stabilization of homogeneous polynomial systems

Author

Iggidr, Abderrahman, Outbib, Rachid, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, 020901 industrial engineering & automation, 010102 general mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], feedback, dilations, 02 engineering and technology, 0101 mathematics, homogeneous systems, 01 natural sciences, Stabilization, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The propose of this paper is to drive a simple necessary and sufficient stabilizability condition for a class of multi-inputs polnomial systems. This result represents a generalization of the main theorems of (Iggidr and Vivalda, 1992). The stabilizing feedbacks are explicitly given.

Published
1995
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23. On the stabilization of continuous and discrete time nonlinear systems

Author

Bensoubaya, Mohamed, Ferfera, Abdelhak, Iggidr, Abderrahman, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
[MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience

Published
1995

24. Etude de la croissance de la Saccharomyces cerevisiae. Contrôle et observation d'un bioprocédé semi-continu

Author

Pengov, Marco, Richard, Edouard, Vivalda, Jean-Claude, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine

Subjects
commande non linéaire, grand gain, observateurs, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], bioprocédé semi-continu, Kalman étendu
Abstract

Le travail présenté dans ce rapport a pour objet l'amélioration de la productivité d'un procédé de fabrication de la levure Saccharomyces cerevisiae et en particulier la synthèse d'observateurs en vue de leur utilisation dans une loi de commande. La première partie de notre étude concerne les propriétés du modèle. On s'intéresse également à la synthèse d'un observateur Grand Gain et à un observateur de type Kalman étendu. Des simulations montrent le comportement dynamique des observateurs proposés.

Published
1995

25. Stabilization of a class of multi-inputs nonlinear systems

Author

Abderrahman Iggidr, Jean-Claude Vivalda, Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
0209 industrial biotechnology, Pure mathematics, Class (set theory), General Computer Science, Mechanical Engineering, 010102 general mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, State (functional analysis), 01 natural sciences, [SPI.AUTO]Engineering Sciences [physics]/Automatic, Nonlinear system, 020901 industrial engineering & automation, Control and Systems Engineering, Control theory, Affine transformation, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Electrical and Electronic Engineering, Equivalence (measure theory), ComputingMilieux_MISCELLANEOUS, Mathematics
Abstract

In this paper, we investigate the local stabilization of affine analytic systems x = f(x) + ∑ i = 1 n − 1 u i g i (x) with n − 1 inputs. We state a sufficient condition on the first approximation of f for which the local asymptotic stabilizability can be achieved; furthermore, we give explicitly the stabilizing feedback.

Published
1994
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26. Nonlinear stabilization by adding integrators

Author

Iggidr, Abderrahman, Sallet, Gauthier, Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS), Geometric control for non-linear systems (CONGE), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
Lyapunov function, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], global stabilization, nonlinear, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; The global stabilization problem of a nonlinear control system with an integrator is considered when the initial system (subsystem without integrator) is stabilizable. It is supposed that the stabilizing feedback and the Lyapunov function for the initial system satisfy the Barbashin-Krasovski\u ı asymptotic stability theorem. Explicit formulae for stabilizing feedback of a nonlinear system with an integrator are derived. The use of Lyapunov functions with derivatives of constant but not fixed signs significantly simplifies the computing of stabilizing feedback. This is confirmed by examples. The global stabilization of a nonlinear control system of the form \dot x= f(x, y), \qquad \qquad \dot y=u \tag 1 is studied, where x∈ \bbfRⁿ, y∈ \bbfR^p, u∈ \bbfR^p and f is a smooth vector field such that f (0, 0) =0. It is proved that to find a feedback stabilizer for this system we do not need to have a strict Lyapunov function for the subsystem (2) \dot x= f(x, v), where v is the input. Moreover, it is proved how to asymptotically stabilize system (1) without stabilizing system (2).

Published
1994

27. Exponential Stabilization of Nonlinear Systems by an Estimated State Feedback

Author

Iggidr, Abderrahman, Sallet, Gauthier, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
non-linear systems, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], observer, feedback, exponential stabilization, Lyapunov functions, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; In this paper we investigate the stabi-lizability problem of a class of multi-input multi-output nonlinear systems which linearization at the origin is controllable and observable. Under assumptions on the nonlinear part we prove : (a) the system is globally exponentially stabilizable (G.E.S) by means of linear feedback law. (b) the system can be G.E.S using a state estimation given by an observer.

Published
1993

28. Integrators and Nonlinear Stabilization

Author

Iggidr, Abderrahman, Sallet, Gauthier, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
0209 industrial biotechnology, 020901 industrial engineering & automation, 020208 electrical & electronic engineering, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 0202 electrical engineering, electronic engineering, information engineering, 02 engineering and technology, ComputingMilieux_MISCELLANEOUS, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience

Published
1992
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29. Local Stabilization of Analytic Systems with n-1 inputs

Author

Iggidr, Abderrahman, Vivalda, Jean-Claude, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine

Subjects
asymptotic stabilization, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], Lyapunov's function, nonlinear systems, Feedback, [SPI.AUTO]Engineering Sciences [physics]/Automatic
Abstract

International audience; In this communication, we investigate the local stabilization of analytic systems ˙ x = f (x) + Bu with n − 1 inputs. We state a sufficient condition on the first approximation of f for which the local asymptotic stabilizability can be achieved; furthermore, we give explicitly the stabilizing feedback.

Published
1992

30. On spectrum assignment of infinite-dimensional linear systems by bounded linear feedback

Author

Xu, Cheng-Zhong, Sallet, Gauthier, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
perturbation, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], bounded linear feedback control, distributed parameter systems, spectral determination, stability, flexible rotating structures
Abstract

This paper deals with the spectrum assignability via bounded linear feedback. The necessary and sufficient condition of Sun is generalized to a class of boundary control systems. A natural application of our theoretical results is briefly presented. The results obtained in this paper have potential applications in non-dissipative spectral systems.

Published
1992

31. Global stabilization of homogeneous polynomial systems in $R^n$

Author

Abderrahman Iggidr, J. C. Vivalda, Laboratoire de Mathématiques et Applications de Metz (LMAM), Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM), INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria), Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), and Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Lyapunov function, 0209 industrial biotechnology, Pure mathematics, Applied Mathematics, 010102 general mathematics, Mathematical analysis, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], 02 engineering and technology, 01 natural sciences, Stability (probability), Matrix polynomial, [SPI.AUTO]Engineering Sciences [physics]/Automatic, symbols.namesake, 020901 industrial engineering & automation, Stable polynomial, Homogeneous polynomial, symbols, Vector field, [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], 0101 mathematics, Analysis, Monic polynomial, Mathematics
Abstract

International audience; This paper deals with a nonlinear control process dx/dt=X(x)+Bu, x∈\bold Rⁿ, u∈ \bold R^n-1, where X(x) is a homogeneous polynomial function. The authors present a necessary and sufficient condition for this system to be globally stabilizable by an analytic in x feedback u(x) (u(0)=0). The stabilizing feedback is constructed explicitly for even and odd functions X(x). Illustrative examples are given. For a control system of the form \dot x=X(x)+Bu, x∈\bbfR\sp n, u∈\bbfR\spn-1, where X is a homogeneous vector field and B a matrix of rank n-1, the problem of global stabilizability by feedback control u=u(x) is considered. A necessary and sufficient condition for such a control is obtained, and an explicit construction of it is given. For polynomials of odd degree this construction is satisfactory, and can also be used for local stabilizability of non-homogeneous polynomials. For even degree, the construction does not work, but the authors promise another future paper for this case.

Published
1992
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32. Condition suffisante pour la stabilisation globale des systèmes en cascade

Author

Outbib, Rachid, Geometric control for non-linear systems (CONGE), Laboratoire Méthodes Mathématiques pour l'Analyse des Systèmes (MMAS), Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-INRIA Lorraine, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), INRIA, and Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-Centre National de la Recherche Scientifique (CNRS)-Université Paul Verlaine - Metz (UPVM)-INRIA Lorraine

Subjects
système non linéaire, exponentiellement asymptotiquement stable, [INFO.INFO-OH]Computer Science [cs]/Other [cs.OH], système de phase minimale faible, intégrateur
Abstract

Dans ce papier, nous proposons une condition sous laquelle un système non linéaire peut être rendu globalement asymptotiquement stable par un feedback régulier. Puis, nous montrons que notre résultat permet d'améliorer le concept des systèmes à phase minimale faible de degré relatif égal à 1 développé récemment, et de généraliser la condition de stabilisation des systèmes obtenus par une cascade d'un système linéaire contrôlable et un système non linéaire général.

Published
1991

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