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Uniformly Lipschitz stability and asymptotic property of perturbed functional differential systems

구윤회|임동만
강원경기수학회 (The Kangweon-Kyungki Mathematical Society)|2016.03|한국수학논문집 (Korean Journal of Mathematics)|제24권 제1호|pp. 1-13|DOI http://dx.doi.org/10.11568/kjm.2016.24.1.1

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키워드

uniformly Lipschitz stabilityuniformly Lipschitz stability in variationexponentially asymptotic stabilityexponentially asymptotic stability in variation.
주제분류수학

초록

This paper shows that the solutions to the perturbed functional differential system\\ \begin{eqnarray*} y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds \end{eqnarray*} have uniformly Lipschitz stability and asymptotic property. To show these properties, we impose conditions on the perturbed part $\int_{t_0}^tg(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y'=f(t,y)$.

Abstract

This paper shows that the solutions to the perturbed functional differential system\\ \begin{eqnarray*} y'=f(t,y)+\int_{t_0}^tg(s,y(s),Ty(s))ds \end{eqnarray*} have uniformly Lipschitz stability and asymptotic property. To show these properties, we impose conditions on the perturbed part $\int_{t_0}^tg(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system $y'=f(t,y)$.

참고문헌 (16)

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관련 논문AI추천

UNIFORMLY LIPSCHITZ STABILITY AND ASYMPTOTIC PROPERTY IN PERTURBED NONLINEAR DIFFERENTIAL SYSTEMS구윤회, Sang Il Choi한국수학교육학회 · 이론수학과 교직수학2016 · 제23권 제1호LIPSCHITZ AND ASYMPTOTIC STABILITY OF PERTURBED FUNCTIONAL DIFFERENTIAL SYSTEMS구윤회, 최상일한국수학교육학회 · 이론수학과 교직수학2015 · 제22권 제1호Boundedness in Perturbed functional differential systems via $t_{\infty}$-similarity구윤회, 최상일강원경기수학회 · 한국수학논문집2015 · 제23권 제2호Lipschitz and asymptotic stability of nonlinear systems of perturbed differential equations구윤회, 최상일강원경기수학회 · 한국수학논문집2015 · 제23권 제1호Boundedness in nonlinear perturbed differential systems via $t_{\infty}$-similarity구윤회, 임동만강원경기수학회 · 한국수학논문집2016 · 제24권 제4호Boundedness in the nonlinear functional differential systems구윤회, 최상일대한수학회 · 대한수학회논문집2015 · 제30권 제4호

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