• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
• /
• pp.227-230
• /
• 1995

Stability of a coupled nonautonomous ordinary differential equation is investigated. Asymptotic convergence to zero of a part of state vector is additionally shown, otherwise only uniform stability could have been concluded by the Lyapunov direct method. Obtained results could be particularly useful in analysis of nonautonomous systems in which the invariance principle does not hold. An illustrating example is given.

• 대한수학회지
• /
• 제37권5호
• /
• pp.805-821
• /
• 2000

The paper deals with asymtotic stabillity of nonlinear nonautinomous systems by Lyapunov's direct method. The proposed Lyapunov-like function V(t, x) needs not be continuous in t and Lipschitz in x in a Banach space. The class of systems considered is allowed to be nonautonomous and infinite-dimensional and we relax the boundedness, the Lipschitz assumption on the system and the definite decrescent condition on the Lyapunov function.

• 대한수학회지
• /
• 제49권1호
• /
• pp.165-185
• /
• 2012

In this paper, the topological entropy and measure-theoretic entropy for nonautonomous dynamical systems are studied. Some properties of these entropies are given and the relation between them is discussed. Moreover, the bounds of them for several particular nonautonomous systems, such as affine transformations on metrizable groups (especially on the torus) and smooth maps on Riemannian manifolds, are obtained.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제8권2호
• /
• pp.87-93
• /
• 2004

The E-Euler process has been proposed for autonomous dynamical systems in [7]. In this paper, the E-Euler process is extended to nonautonomous dynamical systems. When a discrete function is bounded or gradually decreases to ${\epsilon}\;<<\;1$ as $n\;{\rightarrow}\;{\infty}$, it is shown that the relative error converges to a constant or decreases.

• 한국항공우주학회지
• /
• 제39권2호
• /
• pp.137-143
• /
• 2011

중력구배 인공위성의 pitch 운동이 관성 모멘트 비와 편심율에 따라 혼돈계가 될 수 있다. 혼돈계의 경우 운동의 정확한 예측을 위하여 비혼돈계로 전환하는 혼돈계 제어가 필요하다. 혼돈계 제어에는 feedback control system을 사용할 수 있다. 중력구배 인공위성의 pitch 운동의 혼돈계 제어를 위하여, 비선형 pitch 운동 방정식을 선형화를 하여 linear nonautonomous system을 구하고, 이를 근거로 pitch 운동의 혼돈계 제어와 안정화(stabilization)를 위한 제어법칙을 설계하고 원래의 비선형 혼돈계 pitch 운동에 적용하였다. 설계된 pitch 운동 제어계는 두 개의 parameter를 가지는데, 혼돈계 제어와 안정화에 만족할 만한 결과를 보여주었다.

• Journal of applied mathematics & informatics
• /
• 제29권3_4호
• /
• pp.955-967
• /
• 2011

In this paper we have considered a nonautonomous predator-prey model with discrete time delay due to gestation, in which there are two prey habitats linked by isotropic migration. One prey habitat contains a predator and the other (a refuge) does not. Here, we have established some sufficient conditions on the permanence of the system by using in-equality analytical technique. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. We have observed that the per capita migration rate among two prey habitats and the time delay has no effect on the permanence of the system but it has an effect on the global asymptotic stability of this model. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• 충청수학회지
• /
• 제26권3호
• /
• pp.605-613
• /
• 2013

In this paper, we investigate bounds for solutions of perturbed nonlinear differential systems.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권4호
• /
• pp.337-344
• /
• 2011

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.

• 충청수학회지
• /
• 제23권2호
• /
• pp.383-389
• /
• 2010

In this paper, we investigate h-stability of the nonlinear differential systems using the notion of $t_{\infty}$-similarity.

• 충청수학회지
• /
• 제23권4호
• /
• pp.827-834
• /
• 2010

In this paper, we investigate h-stability of the nonlinear perturbed differential systems.