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Sufficient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary System on the Plane in the Critical Case

Sufficient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary... Differential Equations, Vol. 39, No. 2, 2003, pp. 246–255. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 2, 2003, pp. 227–235. Original Russian Text Copyright c 2003 by Masterkov, Rodina. ORDINARY DIFFERENTIAL EQUATIONS Sucient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary System on the Plane in the Critical Case Yu.V.Masterkov and L. I.Rodina Institute for Mathematics and Computer Science, Udmurt State University, Izhevsk, Russia Received May 18, 2001 INTRODUCTION The investigation of null-controllability of nonlinear systems is an important problem in qual- itative theory of control processes. Such systems govern the mathematical models of numerous processes in economics, biology, physics, chemistry, biophysics, and other sciences. It is well know (e.g., see [1{3]) that the system n m x _ = f (x;t;u); (x;t) 2 R  [t ;1);u 2 U  R ; (1) is locally null-controllable if 0 2 intU and the corresponding linear approximation system is null- controllable. It is especially important to analyze local null-controllability in the so-called \critical case" [i.e., the case in which the linear approximation system for system (1) is not completely controllable]. In most papers, this controllability problem in the critical case was considered for stationary systems (e.g., see http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Sufficient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary System on the Plane in the Critical Case

Masterkov, Yu.; Rodina, L.
Differential Equations , Volume 39 (2) – Oct 5, 2004
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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/A:1025109117153
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 2, 2003, pp. 246–255. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 2, 2003, pp. 227–235. Original Russian Text Copyright c 2003 by Masterkov, Rodina. ORDINARY DIFFERENTIAL EQUATIONS Sucient and Necessary Conditions for the Stable Controllability of a Nonlinear Nonstationary System on the Plane in the Critical Case Yu.V.Masterkov and L. I.Rodina Institute for Mathematics and Computer Science, Udmurt State University, Izhevsk, Russia Received May 18, 2001 INTRODUCTION The investigation of null-controllability of nonlinear systems is an important problem in qual- itative theory of control processes. Such systems govern the mathematical models of numerous processes in economics, biology, physics, chemistry, biophysics, and other sciences. It is well know (e.g., see [1{3]) that the system n m x _ = f (x;t;u); (x;t) 2 R  [t ;1);u 2 U  R ; (1) is locally null-controllable if 0 2 intU and the corresponding linear approximation system is null- controllable. It is especially important to analyze local null-controllability in the so-called \critical case" [i.e., the case in which the linear approximation system for system (1) is not completely controllable]. In most papers, this controllability problem in the critical case was considered for stationary systems (e.g., see

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Differential Equations – Springer Journals

Published: Oct 5, 2004

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