You need JavaScript to view this

On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires

Abstract

A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [French] Dans ce travail, on etudie la stabilite absolue des systemes non lineaires utilisant la deuxieme methode de Liapounov en tenant compte des resultats acquis a partir des travaux de V.M. Popov. On fait d'abord un expose des resultats deja etablis, en particulier en ce qui concerne les criteres frequentiels de stabilite absolue pour le cas d'un systeme de commande automatique comportant une seule non linearite. On a prolonge ces resultats jusqu'a l'etablissement de l'existence d'une parabole limite. On fait ensuite une nouvelle utilisation des methodes etudiees, etablissant des criteres de stabilite absolue pour un systeme  More>>
Authors:
Guelman, M [1] 
  1. Commissariat a l'Energie Atomique, 91 - Saclay (France). Centre d'Etudes Nucleaires, services scientifiques
Publication Date:
Sep 01, 1968
Product Type:
Technical Report
Report Number:
CEA-R-3593
Resource Relation:
Other Information: 21 refs; PBD: Sep 1968
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; AUTOMATION; BOUNDARY CONDITIONS; CLOSED-LOOP CONTROL; LAPLACE TRANSFORMATION; LYAPUNOV METHOD; NONLINEAR PROBLEMS; STABILITY; TRANSFER FUNCTIONS
OSTI ID:
20523376
Research Organizations:
CEA Saclay, 91 (France)
Country of Origin:
France
Language:
French
Other Identifying Numbers:
TRN: FR04R3593091431
Availability:
Available from INIS in electronic form
Submitting Site:
FRN
Size:
[61] pages
Announcement Date:

Citation Formats

Guelman, M. On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires. France: N. p., 1968. Web.
Guelman, M. On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires. France.
Guelman, M. 1968. "On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires." France.
@misc{etde_20523376,
title = {On the stability of non-linear systems; Sur la stabilite des systemes non-lineaires}
author = {Guelman, M}
abstractNote = {A study is made of the absolute stability of nonlinear systems, using Liapounov's second method and taking into account the results obtained from V.M. Popov's work. The results already established are first presented, in particular concerning the frequency domain criterions for absolute stability of automatic control systems containing one single non linearity. The results have been extended to show the existence of a limiting parabola. New use is then made of the methods studied for deriving absolute stability criterions for a system containing a different type of non linearity. Finally, the results obtained are considered from the point of view of Aizerman's conjecture. (author) [French] Dans ce travail, on etudie la stabilite absolue des systemes non lineaires utilisant la deuxieme methode de Liapounov en tenant compte des resultats acquis a partir des travaux de V.M. Popov. On fait d'abord un expose des resultats deja etablis, en particulier en ce qui concerne les criteres frequentiels de stabilite absolue pour le cas d'un systeme de commande automatique comportant une seule non linearite. On a prolonge ces resultats jusqu'a l'etablissement de l'existence d'une parabole limite. On fait ensuite une nouvelle utilisation des methodes etudiees, etablissant des criteres de stabilite absolue pour un systeme comportant un type different de non linearite. On etudie enfin les resultats obtenus, dans l'optique de la conjecture de Aizerman. (auteur)}
place = {France}
year = {1968}
month = {Sep}
}