• 충청수학회지
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• 제26권4호
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• pp.831-842
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• 2013

In this paper, we investigate uniform Lipschitz and asymptotic stability for perturbed differential systems using integral inequalities.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.47-62
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• 1997

This paper is concerned with investigating the global as-ymptotic behavior of the zero solution of the initial-boundary value problem for a nonlinear fourth order wave equation, Moreover an esti-mate of the rate of decay of the solutions is obtained.

• 호남수학학술지
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• 제24권1호
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• pp.1-8
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• 2002

In this paper we will show that if E is an injective module over a commutative ring A, then the sequence of sets $Ass_{A}(A/I^{n})^{*(E)}),\;n{\in}N,$ is increasing and ultimately constant. Also we will obtain some results concerning the integral closure of ideals related to some modules.

• 충청수학회지
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• 제3권1호
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• pp.69-81
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• 1990

In this paper we investigate the problem of exponential asymptotic stability (EAS) in perturbed nonlinear systems of the differential system x' = f(t, x). Also, a simple method for constructing Liapunov functions is used to prove a kind of Massera type converse theorem.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제13권3호
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• pp.237-247
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• 2006

In this paper we solve the Hyers-Ulam stability problem for quadratic functional equations on restricted domains, and then obtain an asymptotic behavior of quadratic mappings on restricted domains.

• Journal of applied mathematics & informatics
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• 제5권3호
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• pp.597-606
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• 1998

In the present study we consider a mathematical model of a non-interactive type autotroph-herbivore system in which the amount of autotroph biomass consumed by the herbivore is assumed to follow a Holling type II functional response. We have also incorpo-rated discrete time delays in the numerical response term to represent a delay due to gestation and in the recycling term which represent a delay due to gestation and in the recycling term which represents the time required for bacterial decomposition. We have derived con-dition for global asymptotic stability of the model in the absence of delays. Conditions for delay-induced asymptotic stability of the steady state are also derived. The length of the delay preserving stability has been estimated and interpreted ecologically.

• 제어로봇시스템학회논문지
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• 제9권8호
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• pp.616-622
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• 2003

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded controllers. Using linear matrix inequalities(LMIs) we estimate the ASR and show the exponential stability of the closed-loop control system in the estimated ASR. We give a simple LMI-based algorithm to get estimates of the ASR. We also give a synthesis algorithm to design a switching surface which will make the estimated ASR big. Finally, we give numerical examples in order to show that our method can give better results than the previous ones for a certain class of uncertain variable structure systems with bounded controllers.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1996년도 하계학술대회 논문집 B
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• pp.927-929
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• 1996

In this paper, we considers the problem of designing an observer for bilinear systems with unknown input. A sufficient condition for the asymptotic stability of the proposed observer is derived by means of delectability, invariant zeros, and stable subspace. In sufficient condition, the bound which guarantees the asymptotic stability was derived, which based on the Lyapunov stability. And Observer existing conditions are suggested in various cases. Through a simple example, we derived the observer structure and the bound which guarantees the asymptotic stability.

• 호남수학학술지
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• 제41권1호
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• pp.51-65
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• 2019

In this paper, we give sufficient conditions to guarantee the asymptotic stability of the zero solution to a kind of nonlinear fractional dynamic equations of order ${\alpha}$ (1 < ${\alpha}$ < 2). By using the Krasnoselskii's fixed point theorem in a weighted Banach space, we establish new results on the asymptotic stability of the zero solution provided f (t, 0) = 0, which include and improve some related results in the literature.

• Journal of applied mathematics & informatics
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• 제32권5_6호
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• pp.807-816
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• 2014

The asymptotic behavior of solutions of Lyapunov type matrix Volterra integro differential equation, in which the coefficient matrices are not stable, is studied by the method of reduction.