• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.5
• /
• pp.580-585
• /
• 1999

This paper deals with the stability of discrete time linear systems with time varying delays in state. In this paper, the magnitude of time-varying delays is assumed to be upper-bouded. The stability of discrete time linear systems with time-varying delays in state is related with the stability of discrete time linear systems with constant time delay in state. To show this, a new Lyapunov function is proposed. Using this Lyapunov function, a sufficient condition for the asymptotic stability is derived.

• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.3
• /
• pp.545-556
• /
• 2009

We show that two notions of asymptotic equilibrium and asymptotic equilibrium in variation for nonlinear differential systems are equivalent via $t_{\infty}$-similarity of associated variational systems. Moreover, we study the asymptotic equivalence between nonlinear system and its variational system.

• Journal of applied mathematics & informatics
• /
• v.28 no.3_4
• /
• pp.583-596
• /
• 2010

In this paper, the problem of delay-dependent stability analysis for cellular neural networks systems with time-varying delays was considered. By using a new Lyapunov-Krasovskii function, delay-dependant stability conditions of the delayed cellular neural networks systems are proposed in terms of linear matrix inequalities (LMIs). Examples are provided to demonstrate the reduced conservatism of the proposed stability results.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.429-436
• /
• 2003

We study the asymptotic equivalence between the nonlinear differential system $\chi$'(t) = f(t, $\chi$(t)) and its variational system ν'(t) = f$\chi$(t, 0)ν(t) by using the comparison principle and notion of strong stability.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1075-1085
• /
• 2014

In this paper we investigate asymptotic properties about asymptotic equilibrium and asymptotic equivalence for linear dynamic systems on time scales by using the notion of $u_{\infty}$-similarity. Also, we give some examples to illustrate our results.

• The Pure and Applied Mathematics
• /
• v.11 no.1
• /
• pp.15-22
• /
• 2004

In this paper, we investigate asymptotic stability, oscillation, asymptotic behavior and existence of the period-2 solutions for difference equation $x_{n+1}\;=\;{\alpha}\;+\;\beta{x_{n-1}}^{p}/{x_n}^p$ where ${\alpha}\;{\geq}\;0,\;{\beta}\;>\;0.\;$\mid$p$\mid$\;{\geq}\;1$, and the initial conditions $x_{-1}\;and\;x_0$ are arbitrary positive real numbers.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.4
• /
• pp.445-468
• /
• 2020

A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

• Journal of the Korean Mathematical Society
• /
• v.37 no.5
• /
• pp.835-847
• /
• 2000

We investigate various ${\Phi}$(t)-stability of comparison differential equations and we obtain necessary and/or sufficient conditions for the asymptotic and uniform asymptotic stability of the differential equations x'=f(t, x).

• KIEE International Transaction on Systems and Control
• /
• v.12D no.1
• /
• pp.39-42
• /
• 2002

This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.4
• /
• pp.831-842
• /
• 2013

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