• Journal of applied mathematics & informatics
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• v.8 no.1
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• pp.297-303
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• 2001

In this paper, the problem of the stability analysis for a class of linear neutral systems with time-varying delay is investigated. Using the Lyapunov method, a delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs) is presented. The LMIs can be easily solved by various convex optimization algorithms.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1255-1262
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• 2012

A type of delayed Lotka-Volterra competition reaction-diffusion system is considered. By constructing a new Lyapunov function, we prove that the unique positive steady-state solution is globally asymptotically stable when interspecies competition is weaker than intraspecies competition. Moreover, we show that the stability property does not depend on the diffusion coefficients and time delays.

• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1193-1198
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• 2012

By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.829-840
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• 2001

Generally it is not easy task whether the stable systems governed by nonlinear ordinary differential equations are asymptotically stable or not. This problem often appears in studying a collision and avoidance control problem based on the stability theory. In this paper we devoted to finding conditions that the stable system obtained from the collision and avoidance control problem is asymptotically stable.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1357-1368
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• 2014

This paper is concerned with a reaction-diffusion single species model with harvesting on n-dimensional isotropically growing domain. The model on growing domain is derived and the corresponding comparison principle is proved. The asymptotic behavior of the solution to the problem is obtained by using the method of upper and lower solutions. The results show that the growth of domain takes a positive effect on the asymptotic stability of positive steady state solution while it takes a negative effect on the asymptotic stability of the trivial solution, but the effect of the harvesting rate is opposite. The analytical findings are validated with the numerical simulations.

• International Journal of Control, Automation, and Systems
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• v.3 no.2
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• pp.244-251
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• 2005

In this paper, we study the problem of stabilizing a general nonlinear control system by means of gradient descent control method which is a dynamic feedback control law. In this method, the general nonlinear control system can be considered as an affine nonlinear control systems. Then by using Sontag's formula we investigate the stability (asymptotic) of the general nonlinear control system.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.2
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• pp.237-253
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• 2020

This article studies asymptotic stability of non-auto nomous linear systems with time-dependent coefficient matrices {A(t)}_t∈ℝ. The classical theorem of Levinson has been widely used to science and engineering non-autonomous systems, but systems with defective eigenvalues could not be covered because such a family does not allow continuous diagonalization. We study systems where the family allows to have upper triangulation and to have defective eigenvalues. In addition to the wider applicability, working with upper triangular matrices in place of Jordan form matrices offers more flexibility. We interpret our and earlier works including Levinson's theorem from the perspective of invariant manifold theory.

• Kyungpook Mathematical Journal
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• v.48 no.2
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• pp.173-181
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• 2008

We give the necessary and sufficient conditions for the asymptotic stability of the linear delay difference equation $x_{n+1}\;-\;a^2x_{n-1}\;+\;bx_{n-k}\;=\;0$, n = 0, 1,$\cdots$, where a and b are arbitrary real numbers and k is a positive integer greater than 1. The obtained conditions are given in terms of parameters a and b of difference equations. The method of proof is based on arithematic of complex numbers as well as properties of analytic functions.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.269-282
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• 2005

We study the global asymptotic stability, global attractivity, boundedness character, and periodic nature of all positive solutions and all negative solutions of the difference equation $$x_{n+1}\;=\;{\alpha}-{\frac{x_{n-1}}{x_{n}},\;n=0,1,\;{\cdots}$$, where ${\alpha}\;\in\; R$ is a real number, and the initial conditions $x_{-1},\;x_0$ are arbitrary real numbers.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1827-1840
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• 2013

This paper is concerned with the positive steady states of a diffusive Holling type II predator-prey system, in which two predators and one prey are involved. Under homogeneous Neumann boundary conditions, the local and global asymptotic stability of the spatially homogeneous positive steady state are discussed. Moreover, the large diffusion of predator is considered by proving the nonexistence of non-constant positive steady states, which gives some descriptions of the effect of diffusion on the pattern formation.