• Title, Summary, Keyword: generalized eigenvalue problem

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A Stability Region of Time-varying Perturbations by Using Generalized Eigenvalue Problem (일반화된 고유치 문제를 이용한 시변 섭동의 안정 범위)

  • Lee, Dal-Ho;Han, Hyung-Seok
    • 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.

Alternative approach for the derivation of an eigenvalue problem for a Bernoulli-Euler beam carrying a single in-span elastic rod with a tip-mounted mass

  • Gurgoze, Metin;Zeren, Serkan
    • Structural Engineering and Mechanics
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    • v.53 no.6
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    • pp.1105-1126
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    • 2015
  • Many vibrating mechanical systems from the real life are modeled as combined dynamical systems consisting of beams to which spring-mass secondary systems are attached. In most of the publications on this topic, masses of the helical springs are neglected. In a paper (Cha et al. 2008) published recently, the eigencharacteristics of an arbitrary supported Bernoulli-Euler beam with multiple in-span helical spring-mass systems were determined via the solution of the established eigenvalue problem, where the springs were modeled as axially vibrating rods. In the present article, the authors used the assumed modes method in the usual sense and obtained the equations of motion from Lagrange Equations and arrived at a generalized eigenvalue problem after applying a Galerkin procedure. The aim of the present paper is simply to show that one can arrive at the corresponding generalized eigenvalue problem by following a quite different way, namely, by using the so-called "characteristic force" method. Further, parametric investigations are carried out for two representative types of supporting conditions of the bending beam.

A Recursive Data Least Square Algorithm and Its Channel Equalization Application

  • Lim, Jun-Seok;Kim, Jae-Soo
    • The Journal of the Acoustical Society of Korea
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    • v.25 no.2E
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    • pp.43-48
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    • 2006
  • Abstract-Using the recursive generalized eigendecomposition method, we develop a recursive form solution to the data least squares (DLS) problem, in which the error is assumed to lie in the data matrix only. Simulations demonstrate that DLS outperforms ordinary least square for certain types of deconvolution problems.

Variable Selection in Sliced Inverse Regression Using Generalized Eigenvalue Problem with Penalties

  • Park, Chong-Sun
    • Communications for Statistical Applications and Methods
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    • v.14 no.1
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    • pp.215-227
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    • 2007
  • Variable selection algorithm for Sliced Inverse Regression using penalty function is proposed. We noted SIR models can be expressed as generalized eigenvalue decompositions and incorporated penalty functions on them. We found from small simulation that the HARD penalty function seems to be the best in preserving original directions compared with other well-known penalty functions. Also it turned out to be effective in forcing coefficient estimates zero for irrelevant predictors in regression analysis. Results from illustrative examples of simulated and real data sets will be provided.

Study of two dimensional visco-elastic problems in generalized thermoelastic medium with heat source

  • Baksi, Arup;Roy, Bidyut Kumar;Bera, Rasajit Kumar
    • Structural Engineering and Mechanics
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    • v.29 no.6
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    • pp.673-687
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    • 2008
  • In this paper, a thermo-viscoelastic problem in an infinite isotropic medium in two dimensions in the presence of a point heat source is considered. The fundamental equations of the problems of generalized thermoelasticity including heat sources in a thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace-Fourier transform domain for a two dimensional problem. These equations have been solved by the eigenvalue approach. The results have been compared to those available in the existing literature. The graphs have been drawn for different cases.

Design of suboptimal robust kalman filter using LMI approach (LMI기법을 이용한 준최적 강인 칼만 필터의 설계)

  • 진승희;윤태성;박진배
    • 제어로봇시스템학회:학술대회논문집
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    • pp.1477-1480
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    • 1997
  • This paper is concerned with the design of a suboptimal robust Kalman filter using LMI approach for system models in the state space, which are subjected to parameter uncertainties in both the state and measurement atrices. Under the assumption that augmented system composed of the uncertain system and the state estimation error dynamics should be stable, a Lyapunov inequality is obtained. And from this inequaltiy, the filter design problem can be transformed to the gneric LMI problems i.e., linear objective minimization problem and generalized eigenvalue minimization problem. When applied to uncertain linear system modles, the proposed filter can provide the minimum upper bound of the estimation error variance for all admissible parameter uncertainties.

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Optimal Stacking Sequence Design of Laminated Composites under Buckling Loads (좌굴하중하에서 복합적층판의 최적 적층 설계)

  • 윤성진;김관영;황운봉;하성규
    • Korean Journal of Computational Design and Engineering
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    • v.1 no.2
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    • pp.107-121
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    • 1996
  • An optimization procedure is proposed to determine the optimal stacking sequence on the buckling of laminated composite plates with midplane symmetry under various loading conditions. Classical lamination theory is used for the determination of the critical buckling load of simply supported angle-ply laminates. Analysis is performed by the Galerkin method and Rayleigh-Ritz method. The approximate solution of buckling is replaced by the algorithms that produce generalized eigenvalue problem. Direct search technique is employed to solve the optimization problem effectively. A series of computations is carried out for plates having different aspect ratios, different load ratios and different number of lay-ups.

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Stability Bounds of Time-Varying Uncertainty and Delay Time for Discrete Systems with Time-Varying Delayed State (시변 시간지연을 갖는 이산시스템의 시변 불확실성의 안정 범위)

  • Han, Hyung-Seok
    • Journal of Institute of Control, Robotics and Systems
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    • v.18 no.10
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    • pp.895-901
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    • 2012
  • The stability robustness problem of linear discrete systems with time-varying unstructured uncertainty of delayed states with time-varying delay time is considered. The proposed conditions for stability can be used for finding allowable bounds of timevarying uncertainty and delay time, which are solved by using LMI (Linear Matrix Inequality) and GEVP (Generalized Eigenvalue Problem) known as powerful computational methods. Furthermore, the conditions can imply the several previous results on the uncertainty bounds of time-invariant delayed states. Numerical examples are given to show the effectiveness of the proposed algorithms.

Implementation of Bidirectional Associative Memories Using the GBAM Model with Bias Terms (바이어스항이 있는 GBAM 모델을 이용한 양방향 연상메모리 구현)

  • 임채환;박주영
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • pp.69-72
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    • 2001
  • In this paper, we propose a new design method for bidirectional associative memories model with high error correction ratio. We extend the conventional GBAM model using bias terms and formulate a design procedure in the form of a constrained optimization problem. The constrained optimization problem is then transformed into a GEVP(generalized eigenvalue problem), which can be efficiently solved by recently developed interior point methods. The effectiveness of the proposed approach is illustrated by a example.

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