• Journal of Korea Society of Industrial Information Systems
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• v.11 no.5
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• pp.62-66
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• 2006

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

• Journal of the Korean Mathematical Society
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• v.35 no.2
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• pp.449-463
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• 1998

In this paper we introduce the notions of orbital Lipschitz stability (in variation) and orbital exponential asymptotic stability (in variation) of $C^{r}$ dynamical systems (or $C^{r}$ diffeomor-phisms) on Riemannian manifolds, and study the embedding problem of those concepts in $C^{r}$ dynamical systems.stems.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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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.

• The Pure and Applied Mathematics
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• v.12 no.2 s.28
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• pp.93-103
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• 2005

We study some stability properties and asymptotic behavior for linear difference systems by using the results in [W. F. Trench: Linear asymptotic equilibrium and uniform, exponential, and strict stability of linear difference systems. Comput. Math. Appl. 36 (1998), no. 10-12, pp. 261-267].

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.6
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• pp.492-495
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• 2005

This paper deals with the problem of estimating the asymptotic stability region(ASR) of uncertain variable structure systems with bounded control. Using linear matrix inequalities(LMIs) we estimate the ASR and we show the exponential stability of the closed-loop control system in the estimated ASR. We show that our estimate is always better than the estimate of [3].

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.81-108
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• 2003

We consider the Korteweg-de Vries-Burgers (KdVB) equation on the domain [0,11]. We derive a control law which guarantees $L^2$-global exponential stability, $H^3$-global asymptotic stability, and $H^3$-semiglobal exponential stability.

• Journal of the Korean Mathematical Society
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• v.29 no.1
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• pp.175-190
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• 1992

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.8
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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.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.281-295
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• 2005

The purpose of this paper is to study a class of delay differential equations with two delays. First, we consider the existence of periodic solutions for some delay differential equations. Second, we investigate the local stability of the zero solution of the equation by analyzing the corresponding characteristic equation of the linearized equation. The exponential stability of a perturbed delay differential system with a bounded lag is studied. Finally, by choosing one of the delays as a bifurcation parameter, we show that the equation exhibits Hopf and saddle-node bifurcations.

• The Pure and Applied Mathematics
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• v.18 no.3
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• pp.231-244
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• 2011

We prove the Hyers-Ulam stability for trigonometric type functional inequalities in restricted domains with time variables. As consequences of the result we obtain asymptotic behaviors of the inequalities and stability of related functional inequalities in almost everywhere sense.