• Journal of Institute of Control, Robotics and Systems
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• v.10 no.2
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• pp.145-152
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• 2004

In this paper, an S(stochastic)-eigenvalue and its corresponding S-eigenvector concept for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the stochastic variable parameters in the dynamic model of a plant. An S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue/-eigenvector concept is also proposed. The proposed control design scheme based on the proposed concept is applied to a longitudinal dynamics of an open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure effects. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on the system.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.7-12
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• 2003

In this paper, S(stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties are proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design scheme is applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure.

• Journal of Mechanical Science and Technology
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• v.18 no.6
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• pp.933-945
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• 2004

In this paper, S (stochastic)-eigenvalue concept and its S-eigenvector for linear continuous-time systems with probabilistic uncertainties is proposed. The proposed concept is concerned with the perturbation of eigenvalues due to the probabilistic variable parameters in the dynamic model of a plant. S-eigenstructure assignment scheme via the Sylvester equation approach based on the S-eigenvalue concept is also proposed. The proposed design schemes are illustrated by numerical examples, and applied to the longitudinal dynamics of open-loop-unstable aircraft with possible uncertainties in aerodynamic and thrust effects as well as separate dynamic pressure. These results explicitly characterize how S-eigenvalues in the complex plane may impose stability on S-eigenstructure assignment.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.11
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• pp.901-906
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• 2005

The stability robustness problem of continuous linear systems with nominal and delayed time-varying perturbations is considered. In the previous results, the entire bound was derived only for the overall perturbations without separation of the perturbations. In this paper, the sufficient condition for stability of the system with two perturbations, which are nominal and delayed, is expressed as linear matrix inequalities(LMIs). The corresponding stability bounds fer those two perturbations are determined by LMI(Linear Matrix Inequality)-based generalized eigenvalue problem. Numerical examples are given to compare with the previous results and show the effectiveness of the proposed.

• Structural Engineering and Mechanics
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• v.4 no.3
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• pp.277-301
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• 1996

A finite element model of a beam element with flexible connections is used to investigate the effect of the randomness in the stiffness values on the modal properties of the structural system. The linear behavior of the connections is described by a set of random fixity factors. The element mass and stiffness matrices are function of these random parameters. The associated eigenvalue problem leads to eigenvalues and eigenvectors which are also random variables. A second order perturbation technique is used for the solution of this random eigenproblem. Closed form expressions for the 1st and 2nd order derivatives of the element matrices with respect to the fixity factors are presented. The mean and the variance of the eigenvalues and vibration modes are obtained in terms of these derivatives. Two numerical examples are presented and the results are validated with those obtained by a Monte-Carlo simulation. It is found that an almost linear statistical relation exists between the eigenproperties and the stiffness of the connections.

• Journal of KSNVE
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• v.8 no.3
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• pp.408-419
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• 1998

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. Approach for both qulitative and quantitative analysis of the noise effect in a nonlinear system under harmonic excitation is presented. For the qualitative analysis, Lyapunov exponents are calculated and Poincar map is illustrated. For the quatitative analysis. Fokker-Planck equatin is solved numerical by means of a Path-integral solution procedure. Eigenvalue problem obtained from the numerical caculation is solved and the relation of eigenvalue, eigenvector and chaotic motion is investigated.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.4
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• pp.593-600
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• 2003

Structural optimization often requires the evaluation of design sensitivities. The Semi Analytic Method(SAM) fur computing sensitivity is popular in shape optimization because this method has several advantages. But when relatively large rigid body motions are identified for individual elements. the SAM shows severe inaccuracy. In this study, the improvement of design sensitivities corresponding to the rigid body mode is evaluated by exact differentiation of the rigid body modes. Moreover. the error of the SAM caused by numerical difference scheme is alleviated by using a series approximation for the sensitivity derivatives and considering the higher order terms. Finally the present study shows that the refined SAM including the iterative method improves the results of sensitivity analysis in dynamic problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.1
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• pp.79-92
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• 2000

We investigate numerical properties of Newton's algorithm for improving an eigenpair of a real matrix A using only fixed precision arithmetic. We show that under natural assumptions it produces an eigenpair of a componentwise small relative perturbation of the data matrix A.

• Korean Journal of Mathematics
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• v.7 no.2
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• pp.171-181
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• 1999

We investigate multiplicity of solutions for a nonlinear perturbation of a parabolic operator under Dirichlet boundary condition, in a bounded domain.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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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.