• Title/Summary/Keyword: rank condition

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Rank-preserver of Matrices over Chain Semiring

  • Song, Seok-Zun;Kang, Kyung-Tae
    • Kyungpook Mathematical Journal
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    • v.46 no.1
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    • pp.89-96
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    • 2006
  • For a rank-1 matrix A, there is a factorization as $A=ab^t$, the product of two vectors a and b. We characterize the linear operators that preserve rank and some equivalent condition of rank-1 matrices over a chain semiring. We also obtain a linear operator T preserves the rank of rank-1 matrices if and only if it is a form (P, Q, B)-operator with appropriate permutation matrices P and Q, and a matrix B with all nonzero entries.

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A Test of the Rank Conditions in the Simultaneous Equation Models (연립방정식 모형의 계수조건 검정법 제안)

  • So, Sun-Ha;Park, You-Sung;Lee, Dong-Hee
    • Communications for Statistical Applications and Methods
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    • v.16 no.1
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    • pp.115-125
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    • 2009
  • Simultaneous equation models, which are widely used in business and economic areas, generally consist of endogenous variables determined within models and exogenous variables externally determined and in the simultaneous equations model framework there are rank and order conditions for the model identification and the existence of unique solutions. By contrast, their estimating results have less efficiencies and furthermore do not exist, since the most estimating procedures are performed under the assumptions for rank and order conditions. We propose the new statistical test for sufficiency of the rank condition under the order condition, and show the asymptotic properties for the test. The Monte Carlo simulation studies are achieved in order to evaluate its power and to suggest the baseline for satisfying the rank conditions.

OPERATORS WITH RANK ONE SELFCOMMUTATORS

  • Lee, Jun Ik
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.1
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    • pp.163-168
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    • 2010
  • In this paper it is shown that if [$T^*$,T] is of rank one and ker [$T^*$,T] is invariant for T, then T is quasinormal. Thus, we can know that the hyponormal condition is superfluous in the Morrel's theorem.

Time-delayed State Estimator for Linear Systems with Unknown Inputs

  • Jin Jaehyun;Tahk Min-Jea
    • International Journal of Control, Automation, and Systems
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    • v.3 no.1
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    • pp.117-121
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    • 2005
  • This paper deals with the state estimation of linear time-invariant discrete systems with unknown inputs. The forward sequences of the output are treated as additional outputs. In this case, the rank condition for designing the unknown input estimator is relaxed. The gain for minimal estimation error variance is presented, and a numerical example is given to verify the proposed unknown input estimator.

Design of a reduced-order $H_{\infty}$ controller using an LMI method (LMI를 이용한 축소차수 $H_{\infty}$ 제어기 설계)

  • Kim, Seog-Joo;Chung, Soon-Hyun;Cheon, Jong-Min;Kim, Chun-Kyung;Lee, Jong-Moo;Kwon, Soon-Man
    • Proceedings of the KIEE Conference
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    • 2004.11c
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    • pp.729-731
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    • 2004
  • This paper deals with the design of a low order $H_{\infty}$ controller by using an iterative linear matrix inequality (LMI) method. The low order $H_{\infty}$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the effectiveness of the proposed algorithm.

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Design of a Fixed-Structure H$_{\infty}$ Power System Stabilizer (고정 구조를 가지는$H_\infty$ 전력계통 안정화 장치 설계)

  • Kim Seog-Joo;Lee Jong-Moo;Kwon Soonman;Moon Young-Hyun
    • The Transactions of the Korean Institute of Electrical Engineers A
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    • v.53 no.12
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    • pp.655-660
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    • 2004
  • This paper deals with the design of a fixed-structure $H_\infty$ power system stabilizer (PSS) by using an iterative linear matrix inequality (LMI) method. The fixed-structure $H_\infty$ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, a linear penalty function is incorporated into the objective function so that minimizing the penalized objective function subject to LMIs amounts to a convex optimization problem. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. The proposed algorithm is, therefore, convergent. Numerical experiments show the practical applicability of the proposed algorithm.

Design of a Low-Order H Controller Using an Iterative LMI Method (반복 선형행렬부등식을 이용한 저차원 H 제어기 설계)

  • Kim Chun-Kyung;Kim Kook-Hun;Moon Young-Hyun;Kim Seog-Joo
    • Journal of Institute of Control, Robotics and Systems
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    • v.11 no.4
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    • pp.279-283
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    • 2005
  • This paper deals with the design of a low-order H/sub ∞/ controller by using an iterative linear matrix inequality (LMI) method. The low-order H/sub ∞/ controller is represented in terms of LMIs with a rank condition. To solve the non-convex rank-constrained LMI problem, the recently developed penalty function method is applied. With an increasing sequence of the penalty parameter, the solution of the penalized optimization problem moves towards the feasible region of the original non-convex problem. Numerical experiments showed the effectiveness of the proposed algorithm.

REMARKS ON ULRICH BUNDLES OF SMALL RANKS OVER QUARTIC FOURFOLDS

  • Yeongrak Kim
    • Journal of the Korean Mathematical Society
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    • v.61 no.2
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    • pp.279-291
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    • 2024
  • In this paper, we investigate a few strategies to construct Ulrich bundles of small ranks over smooth fourfolds in ℙ5, with a focus on the case of special quartic fourfolds. First, we give a necessary condition for Ulrich bundles over a very general quartic fourfold in terms of the rank and the Chern classes. Second, we give an equivalent condition for Pfaffian fourfolds in every degree in terms of arithmetically Gorenstein surfaces therein. Finally, we design a computer-based experiment to look for Ulrich bundles of small rank over special quartic fourfolds via deformation theory. This experiment gives a construction of numerically Ulrich sheaf of rank 4 over a random quartic fourfold containing a del Pezzo surface of degree 5.

Multi-Objective Controller Design using a Rank-Constrained Linear Matrix Inequality Method (계수조건부 LMI를 이용한 다목적 제어기 설계)

  • Kim, Seog-Joo;Kim, Jong-Moon;Cheon, Jong-Min;Kwon, Soon-Mam
    • Journal of Institute of Control, Robotics and Systems
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    • v.15 no.1
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    • pp.67-71
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    • 2009
  • This paper presents a rank-constrained linear matrix inequality (LMI) approach to the design of a multi-objective controller such as $H_2/H_{\infty}$ control. Multi-objective control is formulated as an LMI optimization problem with a nonconvex rank condition, which is imposed on the controller gain matirx not Lyapunov matrices. With this rank-constrained formulation, we can expect to reduce conservatism because we can use separate Lyapunov matrices for different control objectives. An iterative penalty method is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method.

The Examination of Load Carrying Capacity Based on Existing Data for Improved Safety Assessment Method of Expressway Bridges (고속도로 교량의 개선된 안전성 평가방안을 위한 실측자료에 기초한 공용 내하력 검토)

  • Lee, Jong Ho;Han, Sung Ho;Sin, Jae Chul
    • KSCE Journal of Civil and Environmental Engineering Research
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    • v.29 no.6A
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    • pp.597-605
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    • 2009
  • The safety of expressway bridges was estimated by checking the external condition rank based on the nondestructive inspection and material test and by measuring load carrying capacity based on the result of load test. Although the load carrying capacity of the bridges was clearly low compared to the design standard, it was examined that many of the bridges have good external condition rank relatively. Also, it can be assured that load carrying capacity shows a considerable difference according to various condition even though the bridges have similar construction year and a structural type. Therefore, this study showed various problems of the current safety measurement of expressway bridges by considering the status of the expressway bridges, external condition rank, and method of safety diagnosis and repair, rehabilitation for maintenance. Based on the existing data of over 400 expressway bridges, the load carrying capacity was analyzed quantitatively considering bridge type, serviced life, design live load, external condition rank and traffic count as variables. The result of this study will be expected to provide the basic information for a reasonable safety assessment of expressway bridge.