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CONVERGENCE OF SOLUTIONS OF TIME-VARYING LINEAR SYSTEMS WITH INTEGRABLE FORCING TERM

Part of: Stability theory

Published online by Cambridge University Press:  01 December 2008

JITSURO SUGIE
JITSURO SUGIE*
Affiliation:
Department of Mathematics and Computer Science, Shimane University, Matsue 690-8504, Japan (email: [email protected])
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Abstract

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The following system is considered in this paper: The primary goal is to establish conditions on time-varying coefficients e(t), f(t), g(t) and h(t) and a forcing term p(t) for all solutions to converge to the origin (0,0) as . Here, the zero solution of the corresponding homogeneous linear system is assumed to be neither uniformly stable nor uniformly attractive. Sufficient conditions are given for asymptotic stability of the zero solution of the nonlinear perturbed system under the assumption that q(t,0,0)=0.

Keywords

nonhomogeneous linear systemsweakly integrally positiveperturbation problems

MSC classification

Secondary: 34D05: Asymptotic properties 34D10: Perturbations 34D20: Stability
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 78 , Issue 3 , December 2008 , pp. 445 - 462
Copyright
Copyright © 2009 Australian Mathematical Society

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