• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.1847-1854
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• 2013

The main concern of this paper is to study the dynamics of an n-dimensional ratio-dependent predator-prey system with diffusion. We study the dissipativeness, persistence of the system and it is shown that the unique positive constant steady state is globally asymptotically stable under some assumptions.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.575-587
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• 2006

In this paper, we provide 3 detailed and explicit procedure of obtaining some regions of attraction for the positive steady state (assumed to exist) of a well known Lotka-Volterra type predator-prey system. Also we obtain the sufficient conditions to ensure that the positive equilibrium point of a well known Lotka-Volterra type predator-prey system with a single discrete delay is globally asymptotically stable.

• Communications of the Korean Mathematical Society
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• v.24 no.1
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• pp.85-97
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• 2009

In this paper we study the existence of global weak solutions for a hyperbolic hemivariational inequalities with boundary source and damping terms, and then investigate the asymptotic stability of the solutions by using Nakao Lemma [8].

• International Journal of Control, Automation, and Systems
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• v.4 no.2
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• pp.172-177
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• 2006

In the networked control system (NCS), the uncertain network-induced delay and nonlinear controlled object are the main problems, because they can degrade the performance of the control system and even destabilize it. In this paper, a class of uncertain and nonlinear networked control systems is discussed and its sufficient condition for the robust asymptotic stability is presented. Further, the maximum network-induced delay that insures the system stability is obtained. The Lyapunov and LMI theorems are employed to investigate the problem. The result of an illustrative example shows that the robust stability analysis is sufficient.

• Journal of the Korean Society for Precision Engineering
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• v.17 no.12
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• pp.121-128
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• 2000

The scope of this paper is focused to the systems which have the time period and they should be necessarily studied in the sense of stability and design method of controller to stabilize the orignal unstable systems. In general, the time periodic systems or the systems having same motions during certain time interval are easily found in rotating motion device, i.e., satellite or helicopter and widely used in factory automation systems. The characteristics of the selected dynamic systems are analyzed with the new stability concept and stabilization control method based on Lyapunov direct method. The new method from Lyapunov stability criteria which satisfies the energy convergence is studied with linear algebraic method. And the numerical procedures are developed with computational programming method to apply to the practical linear periodic systems. The results from this paper demonstrate the usefulness in analysis of the asymptotic stability and stabilization of the unstable linear periodic system by using the developed simulation procedures.

• Proceedings of the KIEE Conference
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• 1998.07b
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• pp.641-643
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• 1998

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-bounded. 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.

• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.1-14
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• 1994

In the recent several years the theory of impulsive differential equations has made a rapid progress (see [1] and [2] and the references there). The questions of stability and periodicity of the solutions of these equations have been elaborated in sufficient details while their asymptotic behaviour has been little studied. In the present paper the asymptotic behaviour of the solutions of linear impulsive differential equations is investigated, generalizing the results of J. W. Macki and J.S. Muldowney, 1970 [3], related to ordinary differential equations without impulses.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1269-1297
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• 2020

In this paper, we consider a two-species parabolic-parabolic-elliptic chemotaxis system with weak competition and a fractional diffusion of order s ∈ (0, 2). It is proved that for s > 2p₀, where p₀ is a nonnegative constant depending on the system's parameters, there admits a global classical solution. Apart from this, under the circumstance of small chemotactic strengths, we arrive at the global asymptotic stability of the coexistence steady state.

• Journal of Mechanical Science and Technology
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• v.15 no.10
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• pp.1356-1368
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• 2001

In this paper, the model reference adaptive control (MRAC) of a flexible structure is investigated. Any mechanically flexible structure is inherently distributed parameter in nature, so that its dynamics are described by a partial, rather than ordinary, differential equation. The MRAC problem is formulated as an initial value problem of coupled partial and ordinary differential equations in weak form. The well-posedness of the initial value problem is proved. The control law is derived by using the Lyapunov redesign method on an infinite dimensional filbert space. Uniform asymptotic stability of the closed loop system is established, and asymptotic tracking, i. e., convergence of the state-error to zero, is obtained. With an additional persistence of excitation condition for the reference model, parameter-error convergence to zero is also shown. Numerical simulations are provided.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.119-122
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• 1996

The recently proposed control method using a Lyapunov-like function can give global asymptotic stability to a system with mismatched uncertainties if the uncertainties are bounded by a known function and the uncontrolled system is locally and asymptotically stable. In this paper, we modify the method so that it can be applied to a system not satisfying the latter condition without deteriorating qualitative performance. The assured stability in this case is uniform ultimate boundedness which is as useful as global asymptotic stability in the sense that it is global and the bound can be taken arbitrarily small. By the proposed control law we can deal with both matched and mismatched uncertain systems. The above facts conclude that Lyapunov-like control method is superior to any other Lyapunov direct methods in its applicability to uncertain systems.