• Computational Structural Engineering
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• v.9 no.4
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• pp.219-228
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• 1996

A method used for measuring the stiffness of hinging reinforced concrete frame structures is developed. The so called Stiffness Measure Method is used to evaluate the tangent stiffness of hinge regions while the structure is responding in nonlinear ranges. Eigenvector methods for nonlinear response have not been especially popular because of the need for regenerating eigenvectors as the time history proceeds. In the present work the eigenvectors sets and corresponding nonlinear state variables, i. e., the tangent stiffnesses of the hinge regions, are stored. There is an expectation that previously generated eigenvectors can be reused as the analysis proceeds. The stiffness measure is used to compare the current tangent stiffnesses of hinge regions with those of previously stored eigenvectors sets. Since eigenvector calculations are diminished the method is effective in reducing computational effort for reinforced concrete frame structures subjected to strong ground motions.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1996.11a
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• pp.230-235
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• 1996

Eigenstructure (eigenvalues/eigenvectors) assignment has been shown to be a useful tool for flight control system design. In the sense of the eigenstructure assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eigenvalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructures is proposed. The biorthogonality condition between the left and right modal matrices of a system as well as the relations between the achievable right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. The proposed design methodology is applied to designing a lateral flight control system for an L-1011 aircraft with disturbances.

• Communications for Statistical Applications and Methods
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• v.10 no.2
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• pp.603-606
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• 2003

The maximum likelihood estimators of the eigenvalues and eigenvectors of $$\Sigma$$_1$^{-1}$$\Sigma$$_2$are shown to be the eigenvalues and eigenvectors of $S$_1$^{1}$S$_2$ under multivariate normality and are explicitly derived. The nature of the eigenvalues and eigenvectors of $$\Sigma$$_1$^{-1}$$\Sigma$$_2$ or their estimators will be uncovered.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.95.1-95
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• 2001

This paper is concerned with a novel S-stability (stochastic-stability) concept in linear time-invariant stochastic systems, where a stochastic mode in dynamics depends on both the external disturbance and the inner-parameter variations. This leads to an EAG (eigenstructure assignment gaussian) problem; that is, the problem of associating S-eigenvalues (stochastic-eigenvalues), S-eigenvectors (stochastic-eigenvectors), and their PDFs (probability density functions) with the stochastic information of the systems with the required stochastic specifications. These results explicitly characterize how S-eigenvalues, S-eigenvectors and their PDFs in the complex plane may impose S-stability on stochastic systems.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.101.1-101.1
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• 2012

Building a relativistic magnetohydrodynamic (RMHD) code based on upwind schemes has been a challenging project, because of the absence of analytic expressions of eigenvalues and eigenvectors. We found analytic expressions of eigenvalues and eigenvectors for adiabatic RMHD flows which are relatively simple and manageable. Especially, our eigenvectors can handle all degenerate points. Using these analytic forms, we built a code based on the total variation diminishing (TVD) scheme, and successfully performed one-dimensional shock tube tests.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.162-167
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• 1994

An effective and disturbance suppressible controller can be obtained by assigning the left eigenstructure (eigenvalues/left eigenvectors) of a system. However, the disturbance decouplability is governed by the right eigenstructure(eigenvalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effective and disturbance suppressible controller, the concurrent assignment scheme of the left and right eigenstructure is proposed. The biorthogonality property between the left and right modal matrices of a system well as the relations between the achievable right modal matrix and states selection matrices are used to develop the scheme. The proposed concurrent eigenstructure assignment scheme guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible(achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the usefulness of the proposed scheme.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.216-221
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• 2010

In this paper, we propose and develop a new algorithm for the principle subspace tracking by orthonormalizing the eigenvectors using an approximation of Gram-Schmidt procedure. We carry out a novel mathematical derivation to show that when this approximated version of Gram-Schmidt procedure is added to a modified form of projection approximation subspace tracking deflation (PASTd) algorithm, the eigenvectors can be orthonormalized within a linear computational complexity. While the PASTd algorithm tries to extracts orthonormalized eigenvectors, the new scheme orthonormalizes the eigenvectors after their extraction, yielding much more tacking efficiency. We apply the new tracking scheme for blind adaptive multiuser detection for non-stationary cellular CDMA environment and use extensive simulation results to demonstrate the performance improvement of the proposed scheme.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.412-419
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• 1993

The transient responses of a linear system having undesired disturbances are dominantly governed by the system's left eigenstructure(eigenvalues/left eigenvectors). In control system design problem of altering the transient response of the system, both the controllability and the disturbance suppressibility, should be considered simultaneously to obtain a robust, effective controller. The controllability of the system may be degraded if the left eigenstructure is chosen to suppress the disturbance, or vice versa. In this paper, first, proposed are a modal disturbance suppressibility measure and an improved version of the modal controllability measure suggested by Hamdan and Nayfeh. Second, a simple and general left eigenstructure assignment scheme, considering both the proposed modal disturbance suppressibility measure and the improved version of modal controllability measure, is suggested. When the previous works are applied to assign the left eigenvectors may differ from the desired ones. But the proposed left eigenstructure assignment scheme makes it possible to achieve the desired colsed-loop eigenvalues exactly, provided the desired left eigenvectors reside in the achievable subspace. In case the desired left eigenvectors do not reside in the achievable subspace, the closed-loop eigenvalues are achieved exactly and the left eigenvectors are assigned to the best possible set of eigenvectors in the least square sense. Finally, a numerical example is included to confirm and demonstrate the usefulness of our propositions and to illustrate the proposed design scheme.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2008.11a
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• pp.604-605
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• 2008

Modal participation factor (MPF) is a widely used in a mode-coupling squeal noise problem for finding the most sensitive component over a complex brake system in a vehicle using eigenvectors of sub-components. This methodology requires the problematic total response of system by the unstable squeal noise at a specific frequency as well as eigenvectors of each component belonging to brake system. In this paper, a unit-force response analysis is performed for intact total system to obtain eigenvectors of each component and then such data is directly used for the contribution analysis of a squeal noise problem. Since the eigenvectors of each component induced from virtual unit-excitation is most reliable owing to the intact boundary condition, it can be expected that the corresponding contribution analysis with MPF also provides a trustworthy result.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.1
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• pp.4-12
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• 1995

In the sense of eigenstructure (eigenvalues/eignenvectors) assignment, the effectiveness and disturbance suppressibility of a controller depend mainly on the left eigenstructure (eignevalues/left eigenvectors) of a system. On the other hand, the disturbance decouplability is governed by the right eigenstructure (eignevalues/right eigenvectors) of the system. In this paper, in order to obtain a disturbance decouplable as well as effetive and disturbance suppressible controller, a concurrent assignment methodology of the left and right eigenstructure is proposed. The biorthogonality condition between the left and right modal matrix and state selection matrices are used to develop the methodology. The proposed concurrent eigenstructure assignment methodology guarantees that the desired eigenvalues are achieved exactly and the desired left and right eigenvectors are assigned to the best possible (achievable) sets of eigenvectors in the least square sense, respectively. A numerical example is presented to illustrate the validity and usefulness of the proposed methodology.