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A criterion for the asymptotic stability of singular differential systems by the linear diagonal approximation

A criterion for the asymptotic stability of singular differential systems by the linear diagonal... ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 8, pp. 1095–1101.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c S.G. Krasovskii, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 8, pp. 1035–1040. ORDINARY DIFFERENTIAL EQUATIONS A Criterion for the Asymptotic Stability of Singular Differential Systems by the Linear Diagonal Approximation S. G. Krasovskii Institute for Mathematics, National Academy of Sciences, Minsk, Belarus Received January 5, 2006 DOI: 10.1134/S0012266106080040 Consider the singular linear system εx ˙ = A(t)x, x ∈ R,t ≥ 0, (1 ) A/ε with bounded continuous coefficient matrix A(t) and a small positive parameter ε multiplying the derivative and the perturbed singular system εy˙ = A(t)y + Q(t)y, y ∈ R,t ≥ 0, (1 ) (A+Q)/ε with piecewise continuous perturbation Q(t), Q(t)≤ δ, t ≥ 0. Starting from the fundamental papers by Tikhonov, numerous papers by Butuzov, Vasil’eva, Fedoryuk, Lomov, Rozov, Mishchenko, Vazov, Shishkin, et al. dealt with the analysis of singularly perturbed systems of a more general form. Necessary and sufficient conditions for all solutions y (t, y ,ε), y (0,y ,ε)= y ∈ R ,of sys- 0 0 0 tem (1 ) with continuous matrix A(t)=diag [a (t),... ,a (t)] and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

A criterion for the asymptotic stability of singular differential systems by the linear diagonal approximation

Krasovskii, S.
Differential Equations , Volume 42 (8) – Oct 7, 2006
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References (5)

Publisher
Springer Journals
Copyright
Copyright © 2006 by Pleiades Publishing, Inc.
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266106080040
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2006, Vol. 42, No. 8, pp. 1095–1101.  c Pleiades Publishing, Inc., 2006. Original Russian Text  c S.G. Krasovskii, 2006, published in Differentsial’nye Uravneniya, 2006, Vol. 42, No. 8, pp. 1035–1040. ORDINARY DIFFERENTIAL EQUATIONS A Criterion for the Asymptotic Stability of Singular Differential Systems by the Linear Diagonal Approximation S. G. Krasovskii Institute for Mathematics, National Academy of Sciences, Minsk, Belarus Received January 5, 2006 DOI: 10.1134/S0012266106080040 Consider the singular linear system εx ˙ = A(t)x, x ∈ R,t ≥ 0, (1 ) A/ε with bounded continuous coefficient matrix A(t) and a small positive parameter ε multiplying the derivative and the perturbed singular system εy˙ = A(t)y + Q(t)y, y ∈ R,t ≥ 0, (1 ) (A+Q)/ε with piecewise continuous perturbation Q(t), Q(t)≤ δ, t ≥ 0. Starting from the fundamental papers by Tikhonov, numerous papers by Butuzov, Vasil’eva, Fedoryuk, Lomov, Rozov, Mishchenko, Vazov, Shishkin, et al. dealt with the analysis of singularly perturbed systems of a more general form. Necessary and sufficient conditions for all solutions y (t, y ,ε), y (0,y ,ε)= y ∈ R ,of sys- 0 0 0 tem (1 ) with continuous matrix A(t)=diag [a (t),... ,a (t)] and

Journal

Differential Equations – Springer Journals

Published: Oct 7, 2006

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