• Korean Journal of Mathematics
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• 제22권1호
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• pp.123-131
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• 2014

The purpose of this paper is to study the perturbation analysis of the matrix equation $X=I-A^*X^{-1}A+B^*X^{-1}B$. Based on the matrix differentiation, we give a precise perturbation bound for the positive definite solution. A numerical example is presented to illustrate the shrpness of the perturbation bound.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 춘계학술대회 논문집 전력기술부문
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• pp.17-19
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• 2001

In this paper, eigenvalue perturbation theory and its applications for the augmented system matrix are described. This theory is quite useful in the cases where any change in a system parameter results in signifiant changes to most of the elements of the augmented matrix or where the forming of sensitivity matrix so complicate. And AMEP(augmented matrix eigenvalue perturbation) for the excitation system parameters are computed for analysis of small signal stability of KEPCO 215-machine 791-bus system.

• 제어로봇시스템학회논문지
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• 제1권2호
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제11권1호
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• pp.171-192
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• 2017

The change of any element in the network is possible to cause performance degradation of the multicast network. So it is necessary to optimize the topology path through the multicast update strategy, which directly affects the performance and user experience of the overlay multicast. In view of the above, a new multicast tree update strategy based on perturbation theory Musp (Multicast Update Strategy based on Perturbation theory) is proposed, which reduces the data transmission interruption caused by the multicast tree update and improves user experiences. According to the multicast tree's elements performance and the topology structure, the Musp strategy defines the multicast metric matrix and based on the matrix perturbation theory it also defines the multicast fluctuation factor. Besides it also demonstrates the calculability of the multicast fluctuation factor presents the steps of the Musp algorithm and calculates the complexity. The experimental results show that compared with other update strategies, as for the sensitivity of the multicast fluctuation factor's energized multicast tree to the network disturbance, the maximum delay of the Musp update strategy is minimal in the case of the local degradation of network performance.

• Steel and Composite Structures
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• 제8권2호
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• pp.129-144
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• 2008

This paper demonstrates an application of the perturbation based stochastic finite element method (SFEM) for predicting the performance of structural systems made of composite sections with random material properties. The composite member consists of materials in contact each of which can surround a finite number of inclusions. The perturbation based stochastic finite element analysis can provide probabilistic behavior of a structure, only the first two moments of random variables need to be known, and should therefore be suitable as an alternative to Monte Carlo simulation (MCS) for realizing structural analysis. A summary of stiffness matrix formulation of composite systems and perturbation based stochastic finite element dynamic analysis formulation of structural systems made of composite sections is given. Two numerical examples are presented to illustrate the method. During stochastic analysis, displacements and sectional forces of composite systems are obtained from perturbation and Monte Carlo methods by changing elastic modulus as random variable. The results imply that perturbation based SFEM method gives close results to MCS method and it can be used instead of MCS method, especially, if computational cost is taken into consideration.

• 전산구조공학
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• 제5권3호
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• pp.119-126
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• 1992

교량, 발전소, 해양구조물과 같은 토목구조물은 사용기간중에 지진, 바람, 파랑하중등에 의해 구조적 손상을 받기 쉽다. 장기간에 걸쳐 구조물에 손상이 누적되면 구조물 전체의 파괴를 초래할 수도 있다. 따라서 현존하는 구조물의 안전성을 분석하기 위한 구조물의 손상도를 추정하는 방법이 필요하다. 본 논문에서는 Inverse Modal Perturbation기법을 이용하여 구조물의 손상도를 추정하는 방법에 대하여 연구하였다. Perturbation식은 구조물의 강성 및 질량행렬의 변화량과 구조물의 고유진동수와 모우드형상의 변화량의 식으로 구성된다. 또한 구조물의 손상은 강성행렬의 변화량으로 표현하였다. 본 연구에서는 구조물의 손상도추정의 효율성을 증대시키기 위하여 2차-Perturbation식을 구성하고, 이것을 반복적인 절차를 거쳐 해를 구하는 방법에 대하여 연구하였다. 제안된 방법의 효율성은 일련의 예제해석을 통하여 검증하였으며, 추정된 결과로 부터 본 방법이 구조물의 손상을 적절히 산정함을 알 수 있었다.

• 한국정보통신학회논문지
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• 제23권12호
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• pp.1638-1643
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• 2019

본 논문에서는 MIMO (Multiple-Input Multiple Output, 다중입출력) 시스템을 위한 적응형 섭동을 이용한 기회적 프리코딩(Adaptive Perturbation-aided Opportunistic Precoding) 방식을 제안한다. 제안 프리코딩 방식에서는 MIMO 시스템을 위한 프리코딩 행렬을 생성할 때 랜덤한 섭동 뿐 아니라 사용자로부터 받은 전송률 정보에 의해 결정되는 적응적 변화값을 함께 이용한다. 이전 시간의 랜덤 섭동이 전송속도를 상승시켰을 경우 적응형 섭동을 이전 랜덤 섭동과 동일하게 하고, 그렇지 않을 경우 이전 랜덤한 섭동 값의 음의 값에 해당하는 값을 적용시킨다. 또한 전송 속도 최적화를 위해 스케줄링에서 현재 생성된 프리코딩 행렬 뿐 아니라 메모리에 저장된 최근 프리코딩 행렬 정보도 함께 이용한다. 모의실험 결과에서 기존 프리코딩 방식에 비해 제안한 섭동 기반 기회적 프리코딩 방식이 높은 전송속도를 얻으며, 특히 사용자의 수가 적은 환경에서 전송 속도 이득이 큰 것을 확인할 수 있다.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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• pp.655-663
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• 2012

Based on the elegant properties of the spectral norm and Thompson metric, we firstly give two perturbation estimates for the positive definite solution of the nonlinear matrix equation $$X-\sum^m_{i=1}A^{\ast}_iX^{\delta_i}A_i=Q(0<|{\delta}_i|<1)$$ which arises in an optimal interpolation problem.

• 제어로봇시스템학회논문지
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• 제13권2호
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• pp.147-153
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• 2007

The stability robustness problem of linear discrete-time systems with delayed time-varying perturbations is considered. Compared with continuous time system, little effort has been made for the discrete time system in this area. In the previous results, the bounds were derived for the case of non-delayed perturbations. There are few results for delayed perturbation. Although the results are for the delayed perturbation, they considered only the time-invariant perturbations. In this paper, the sufficient conditions for stability can be expressed as linear matrix inequalities(LMIs). The corresponding stability bounds are determined by LMI(Linear Matrix Inequality)-based algorithms. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed results.

• Structural Engineering and Mechanics
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• 제26권2호
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• pp.163-178
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• 2007

In practical engineering, the uncertain concept plays an important role in the control problems of the vibration structures. In this paper, based on matrix perturbation theory and interval finite element method, the closed-loop vibration control system with uncertain parameters is discussed. A new method is presented to develop an algorithm to estimate the upper and lower bounds of the real parts and imaginary parts of the complex eigenvalues of vibration control systems. The results are derived in terms of physical parameters. The present method is implemented for a vibration control system of the frame structure. To show the validity and effectiveness, we compare the numerical results obtained by the present method with those obtained by the classical random perturbation.