• The Transactions of the Korean Institute of Electrical Engineers
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• v.36 no.4
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• pp.301-304
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• 1987

The Optimal Control Problems for the singular system with the Generalized state space model are considered. It is shown that when the system is singular, the dimension can be reduced by coordinate transformation and the equivalent nonsingular system is got. After we have nonsingular system, the solution for the optimal control problem can be got by Riccati equation.

• Microbiology and Biotechnology Letters
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• v.27 no.3
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• pp.223-229
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• 1999

The two optimal control algorithms, singular approximation and minimum principle, were compared in this paper. The switching time with singular approximation was determined with mathematical derivation and the optimal control profile of specific growth rate was also calculated with minimum principle. The optimal control profiles were calculated by making simple model correlating the specific cell growth rate and specific product formation rate. The optimal control profiles calculated by singular approximation approach were similar to stepwise form of those calculatd by minimum principles. With the minimum principle, the product concentration was 8% more than that of singular approximation. This performance difference was due to a linearization of a nonlinear function with singular approximation. This optimal approaches were applicable to any system with different optimal cell growth and product formation.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.621-638
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• 2009

The linear system Ax = b will have (i) no solution, (ii) only one non-trivial (trivial) solution, or (iii) infinity of solutions. Our focus will be on cases (ii) and (iii). The mathematical models of many real-world problems give rise to (a) ill-conditioned linear systems, (b) singular linear systems (A is singular with all its linearly independent rows are sufficiently linearly independent), or (c) ill-conditioned singular linear systems (A is singular with some or all of its strictly linearly independent rows are near-linearly dependent). This article highlights the scope and need of a randomized algorithm for ill-conditioned/singular systems when a reasonably narrow domain of a solution vector is specified. Further, it stresses that with the increasing computing power, the importance of randomized algorithms is also increasing. It also points out that, for many optimization linear/nonlinear problems, randomized algorithms are increasingly dominating the deterministic approaches and, for some problems such as the traveling salesman problem, randomized algorithms are the only alternatives.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2012.04a
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• pp.324-329
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• 2012

Isolation tables are widely used for precision equipments and their isolation performances have been usually expressed and evaluated by transsmissibility. However, transmissibility is a concept for 1-degree of freedom(DOF) system. In practice, isolation tables are supproted by more than 4 springs. Each spring is subjected to vertical and horizontal ground vibrations, and also the table has more than 1-DOF. Therefore, isolation tables should be treated as multi-input/multi-output(MIMO) system of which isolation performance is expressed by transmissibility matrix. However, the matrix is too complicated to be an index for a system. In this paper, maximum singular value of transmissibility matrx is suggested as a simple performance index of a MIMO isolation system. Physical meaning of singular value is explained using a simple a 2-DOF isolation table. Furthermore, maximum singular values of passive, 3-DOF active and 6-DOF active isolation tables are obtained through experiments, and their meaning are explained and compared with each other.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.877-894
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• 2013

In this paper, we study the existence and uniqueness of solutions for a singular system of nonlinear fractional differential equations with integral boundary conditions. We obtain existence and uniqueness results of solutions by using the properties of the Green's function, a nonlinear alternative of Leray-Schauder type, Guo-Krasnoselskii's fixed point theorem in a cone. Some examples are included to show the applicability of our results.

• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.327-342
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• 2015

By employing a fixed point theorem in a weighted Banach space, we establish the existence of a solution for a system of impulsive singular fractional differential equations. Some examples are presented to illustrate the efficiency of the results obtained.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• v.1
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• pp.133-138
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• 2006

Singular value decomposition (SDV) approach is applied to the observability analysis of GPS/INS in this paper. A measure of observability for a subspace is introduced. It indicates the minimum size of perturbation in the information matrix that makes the subspace unobservable. It is shown that the measure has direct connections with observability of systems, error covariance, and singular structure of the information matrix. The observability measure given in this paper is applicable to the multi-input/multi-output time-varying systems. An example on the observability analysis of GPS/INS is given. The measure of observability is confirmed to be less sensitive to system model perturbation. It is also shown that the estimation error for the vertical component of gyro bias can be considered unobservable for small initial error covariance for a constant velocity horizontal motion.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.46 no.5
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• pp.22-28
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• 2009

In this paper, we consider the problem of $H_{\infty}$ filtering for continuous-time singular systems with multiple state-delays. The aim of designed filter is to guarantee regularity, impulse-free, asymptotic stability and $H_{\infty}$ norm bound of filtering error singular system. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent BRL (bounded real lemma) for singular systems with multiple state-delays is derived. Based on the result, the existence condition of $H_{\infty}$ filter and filter design method are proposed in terms of LMI (linear matrix inequality). Finally, a numerical example is provided to show the validity of the design methods.

• Journal of the Korean Mathematical Society
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• v.39 no.6
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• pp.913-930
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• 2002

For curved crack problems in plane elasticity, subjected to the traction conditions on the crack faces, we present a system of boundary integral equations. The procedure is based on the indirect boundary integral method in terms of real variables. For efficient mathematical analysis, we decompose the singular kernel into the Cauchy singular part and the regular one. As a result, solvability of the presented system is proved and availability of the present approach is shown by the numerical example of a circular arc crack.

• Journal of Institute of Control, Robotics and Systems
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• v.10 no.4
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• pp.364-370
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• 2004

In this paper, we propose a FDI method, which comes from singular value decomposition of measurement matrix fur redundant sensors. We analyze the performance of the proposed FDI method by comparing with the GLT method in two ways such as FDI performance and GN＆C performance. Also, we propose a GN＆C performance index by combining FDI and GN＆C performance.