• Journal of the Korean Society of Safety
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• v.21 no.2 s.74
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• pp.143-149
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• 2006

This paper deals with the space-time finite element analysis of two-dimensional vibration problem with a single variable. The method of space-time finite elements enables the simpler solution than the usual finite element analysis with discretization in space only. We present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period. The weighted residual process is used to formulate a finite element method for a space-time domain. A stability problem is described and some investigations for chosen type of rectangular space-time finite elements are carried out. Instability is caused by a too large time step of successive time steps in the traditional time-dependent problems. It has been shown that the numerical stability of time-stepping on the larger time steps is quite good. The unstructured space-time finite element not only overcomes the shortcomings of the stability in the traditional numerical methods, but it is also endowed with the features of an effective computational technique. Some numerical examples have been presented to illustrate the efficiency of the described method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.64 no.11
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• pp.1598-1604
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• 2015

In this paper, we treat the problem of a robust finite-time dissipative state feedback controller design method for discrete-time singular systems with polytopic uncertainties. A BRL(bounded real lemma) for finite-time stability of discrete-time singular systems is derived. A finite-time dissipative state feedback controller design method satisfying finite-time stability and dissipativity is proposed by LMI(linear matrix inequality) technique on the basis of the obtained BRL. Moreover it is shown that the obtained condition can be extended into polytopic uncertain systems by proper manipulations. Finally, illustrative examples are given to show the applicability of the proposed method.

• Proceedings of the KIEE Conference
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• 1999.11c
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• pp.533-536
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• 1999

We consider digital implementation problems of continuous-time controllers. In general, digital controllers use fixed point representation of number and of finite word length(FWL). Under these conditions, this paper investigates the closed-loop stability caused by three design constraints; (i) finite precision representation of the controller parameters, (ii) realization forms such as direct form, cascade form, and parallel form, and (iii) sampling time. We calculate the coefficient stability margins of both predesigned controllers and controller to be implemented. This method can be applied to determine the word length, realization structure, and sampling time so that remains the stability.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2022.11a
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• pp.168-169
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• 2022

In this study, we investigates the auto-berthing problem for the underactuated surface vessel in the presence of constraints of dynamic uncertainties, finite time, transmission load, and environmental disturbance. A novel control scheme is proposed by fusing the finite time control technology and the event-triggered input algorithm. In the algorithm, differential homeomorphism coordinate the transformation is used to solve the problem of underactuation. Then, we apply the finite time technology and event triggered to save the time of the berthing vessel and relieve transmission burden between the controller and the vessel respectively. Moreover, a radial basis function network is used to approximate unknown nonlinear functions, and minimum learning parameters are introduced to lessen the computational complexity. A sufficient effort has been made to verify the stability of the closed-loop system based on the Lyapunov stability theory. Finally, simulation results display the effectiveness of the proposed scheme.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.2
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• pp.7-14
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• 2009

In this paper we consider the problem of global finite-time stabilization for a class of uncertain nonlinear systems which include uncertainties. The uncertainties are time-varying disturbances or parameters belong to a known compact set. The proposed design method is based on backstepping and dynamic exponent scaling using an augmented dynamics, from which, a dynamic smooth feedback controller is derived. The finite-time stability of the closed-loop system and boundedness of the controller are preyed by the finite-time Lyapunov stability theory and a new notion 'degree indicator'.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.19 no.1 s.71
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• pp.39-46
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• 2006

This paper analyzes the continuous Galerkin method for the space-time discretization of wave equation. The method of space-time finite elements enables the simple solution than the usual finite element analysis with discretization in space only. We present a discretization technique in which finite element approximations are used in time and space simultaneously for a relatively large time period called a time slab. The weighted residual process is used to formulate a finite element method for a space-time domain. Instability is caused by a too large time step in successive time steps. A stability problem is described and some investigations for chosen types of rectangular space-time finite elements are carried out. Some numerical examples prove the efficiency of the described method under determined limitations.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.283-286
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• 1995

Due to finite bandwidth of missile dynamics, guidance commands in PN guidance tend to diverage as the missile approaches to the target. In this paper, a new method based on the short-time stability theorem is introduced to extend the stability region.

• Communications of the Korean Mathematical Society
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• v.29 no.4
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• pp.505-518
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• 2014

Considered here is the first initial boundary value problem for the two-dimensional g-Navier-Stokes equations in bounded domains. We first study the long-time behavior of strong solutions to the problem in term of the existence of a global attractor and global stability of a unique stationary solution. Then we study the long-time finite dimensional approximation of the strong solutions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.22 no.4
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• pp.253-287
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• 2018

This paper studies the global stability of a class of discrete-time pathogen infection models with latently infected cells. The rate of pathogens infect the susceptible cells is taken as bilinear, saturation and general. The continuous-time models are discretized by using nonstandard finite difference scheme. The basic and global properties of the models are established. The global stability analysis of the equilibria is performed using Lyapunov method. The theoretical results are illustrated by numerical simulations.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2008.04a
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• pp.20-25
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• 2008

The finite element analysis for porous media is severe job because constituents have different physical peoperties, and element's continuity and stability should be considered. Thus, we propose the new mixed finite element method in order to overcome the problems. In this method, multi time step, remeshing step, and sub iteration step are introduced. The multi time step and remeshing step make it possible to satisfy a stability and an accuracy during sub iteration in which global time is determined. Finally, the proposed method is compared with the ABAQUS(2007) software and exact solution(Schiffman 1967) through two dimensional consolidation model.