• Structural Engineering and Mechanics
• /
• v.5 no.4
• /
• pp.415-431
• /
• 1997

Stability equations that evaluate the elastic critical axial load of stepped columns under extreme and intermediate concentrated axial loads in any type of construction with sidesway totally inhibited, partially inhibited and uninhibited are derived in a classical manner. These equations can be utilized in the stability analysis of framed structures (totally braced, partially braced, and unbraced) with stepped columns with rigid, semirigid, and simple connetions. The proposed column classification and the corresponding stability equations overcome the limitations of current methods which are based on a classification of braced and unbraced columns. The proposed stability equations include the effects of: 1) semirigid connections; 2) step variation in the column cross section at the point of application of the intermediate axial load; and 3) lateral and rotational restraints at the intermediate connection and at the column ends. The proposed method consists in determining the eigenvalue of a $2{\times}2$ matrix for a braced column at the two ends and of a $3{\times}3$ matrix for a partially braced or unbraced column. The stability analysis can be carried out directly with the help of a pocket calculator. The proposed method is general and can be extended to multi-stepped columns. Various examples are include to demonstrate the effectiveness of the proposed method and to verify that the calculated results are exact. Definite minimum bracing criteria for single stepped columns is also presented.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.21 no.6
• /
• pp.634-639
• /
• 2020

In general, the stability and response characteristics of the system can be improved by changing the pole position because a nonlinear system can be linearized by the product of a 1st and 2nd order system. Therefore, a controller that moves the pole can be designed in various ways. Among the other methods, LQ control ensures the stability of the system. On the other hand, it is difficult to specify the location of the pole arbitrarily because the desired response characteristic is obtained by selecting the weighting matrix by trial and error. This paper evaluated a method of selecting a weighting matrix of LQ control that moves multiple double poles with Jordan blocks to real poles. The relational equation between the double poles and weighting matrices were derived from the characteristic equation of the Hamiltonian system with a diagonal control weighting matrix and a state weighting matrix represented by two variables (ρ_d, ϕ_d). The Moving-Range was obtained under the condition that the state-weighting matrix becomes a positive semi-definite matrix. This paper proposes a method of selecting poles in this range and calculating the weighting matrices by the relational equation. Numerical examples are presented to show the usefulness of the proposed method.

• Management Science and Financial Engineering
• /
• v.8 no.1
• /
• pp.1-19
• /
• 2002

Ordering is used to reduce the amount of fill-ins in the Cholesky factor of a symmetric positive definite matrix. One of the most efficient ordering methods is the minimum degree ordering algorithm(MDO). In this paper, we provide a few techniques that improve the performance of MDO implemented with the clique storage scheme. First, the absorption of nodes in the cliques is developed which reduces the number of cliques and the amount of storage space required for MDO. Second, we present a modified minimum degree ordering algorithm of which the number of degree updates can be reduced by introducing the lower bounds of degrees. Third, using both the lower and upper bounds of degrees, we develop an approximate minimum degree ordering algorithm. Experimental results show that the proposed algorithm is competitive with the minimum degree ordering algorithm that uses quotient graphs from the points of the ordering time and the nonzeros in the Cholesky factor.

• 제어로봇시스템학회:학술대회논문집
• /
• 1996.10a
• /
• pp.48-51
• /
• 1996

This note considers the $H^{\infty}$ controller design problem for linear systems with time-varying delays in states. We obtain sufficient conditions for the existence of k-th order $H^{\infty}$ controllers in terms of three linear matrix ineualities(LMIs). These sufficient conditions are dependent on the maximum value of the time derivative of time-varying delay. Furthermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give an example.e.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.688-691
• /
• 1997

This paper presents an $H^{\infty}$ controller design method for linear time-invariant systems with delayed state and control. Using the second method of Lyapunov, the stability for delayed systems is discussed. For delayed systems, we derive a sufficient condition of the bounded real lemma(BRL) which is similar to BRL for nondelayed systems. And the sufficient conditions for the existence of an output feedback $H^{\infty}$ controller of any order are given in terms of three linear matrix inequalities(LMls). Futhermore, we briefly explain how to construct such controllers from the positive definite solutions of their LMIs and give a simple example to illustrate the validity of the proposed design procedure.e.

• 제어로봇시스템학회:학술대회논문집
• /
• 1993.10b
• /
• pp.355-359
• /
• 1993

This paper deals with the problem of robust TDF(Two Degree of Freedom) H$_{\infty}$ control design for a linear system with parameter uncertainty in the state space model. The uncertain system considered here is with the time-invariant norm-bounded parameter uncertainty in the state matrix. A TDF H$_{\infty}$ control design is presented which robustly stabilizes the plant, guarantees the robust H$_{\infty}$ performance and improves the tracking performance for the closed-loop system in the face of parameter uncertainty. It is shwon that a suitable stabilizing control law can be constructed in terms of a positive definite solution to a certain parameter-dependent algebraic Riccati equation and a good tracking performance can be constructed in terms of suitable feedforward control law.aw.

• Journal of applied mathematics & informatics
• /
• v.29 no.5_6
• /
• pp.1167-1178
• /
• 2011

In this paper, we further investigate the local Hermitian and skew-Hermitian splitting (LHSS) iteration method and the modified LHSS (MLHSS) iteration method for solving generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. When A is non-symmetric positive definite, the convergence conditions are obtained, which generalize some results of Jiang and Cao [M.-Q. Jiang and Y. Cao, On local Hermitian and Skew-Hermitian splitting iteration methods for generalized saddle point problems, J. Comput. Appl. Math., 2009(231): 973-982] for the generalized saddle point problems to generalized nonsymmetric saddle point problems with nonzero (2,2) blocks. Numerical experiments show the effectiveness of the iterative methods.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.26 no.11
• /
• pp.2312-2321
• /
• 2002

The first-order least-squares meshfree method for linear elasticity is presented. The conventional and the compatibility-imposed least-squares formulations are studied on the convergence behavior of the solution and the robustness to integration error. Since the least-squares formulation is a type of mixed formulation and induces positive-definite system matrix, by using shape functions of same order for both primal and dual variables, higher rate of convergence is obtained for dual variables than Galerkin formulation. Numerical examples also show that the presented formulations do not exhibit any volumetric locking for the incompressible materials.

• Journal of applied mathematics & informatics
• /
• v.28 no.1_2
• /
• pp.515-521
• /
• 2010

In multivariate analysis, the inversion formula of the Stieltjes transform is used to find the density of a spectral distribution of random matrices of sample covariance type. Let $B_n\;=\;\frac{1}{N}Y_nY_n^TT_n$ where $Y_n\;=\;[Y_{ij}]_{n\;{\times}\;N}$ is with independent, identically distributed entries and $T_n$ is an $n\;{\times}\;n$ symmetric non-negative definite random matrix independent of the $Y_{ij}$'s. In the present paper, using the inversion formula of the Stieltjes transform, we will find that the limiting distribution of $B_n$ has a continuous density function away from zero.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.57 no.10
• /
• pp.1854-1860
• /
• 2008

In this paper, we deal with the problem of delay-dependent robust and non-fragile stabilization for descriptor systems with parameter uncertainties and time-varying delays on the basis of strict LMI(linear matrix inequality) technique. Also, the considering controller is composed of multiplicative uncertainty. The delay-dependent robust and non-fragile stability criterion without semi-definite condition and decomposition of system matrices is obtained. Based on the criterion, the problem is solved via state feedback controller, which guarantees that the resultant closed-loop system is regular, impulse free and stable in spite of all admissible parameter uncertainties, time-varying delays, and controller fragility. Numerical examples are presented to demonstrate the effectiveness of the proposed method.