• International Journal of Control, Automation, and Systems
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• v.6 no.2
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• pp.288-294
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• 2008

Motivated by the fact that upper solution bounds for the continuous Lyapunov equation are valid under some very restrictive conditions, an attempt is made to extend the set of Hurwitz matrices for which such bounds are applicable. It is shown that the matrix set for which solution bounds are available is only a subset of another stable matrices set. This helps to loosen the validity restriction. The new bounds are illustrated by examples.

• 제어로봇시스템학회:학술대회논문집
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• 1993.10b
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• pp.425-427
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• 1993

Some upper bounds for the solution of the continuous algebraic Riccati equation are presented. These consist of bounds for summations of eigenvalues, products of eigenvalues, individual eigenvalues and the minimum eigenvalue of the solution matrix. Among these bounds, the first three are the first results for the upper bound of each case, while bounds for the minimum eigenvalue supplement the existing ones and require no side conditions for their validities.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.3
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• pp.145-156
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• 2002

Business managers are often required to use LP problems to deal with uncertainty inherent in decision making due to rapid changes in today＇s business environments. Uncertain parameters can be easily formulated in the two-stage stochastic LP problems. However, since solution methods are complex and time-consuming, a common approach has been to use modified formulations to provide upper and lower bounds on the two-stage stochastic LP problem. One approach is to use an expected value problem, which provides upper and lower bounds. Another approach is to use “walt-and-see” problem to provide upper and lower bounds. The objective of this paper is to propose a modified approach of “wait-and-see” problem to provide an upper bound and to compare the relative error of optimal value with various upper and lower bounds. A computing experiment is implemented to show the relative error of optimal value with various upper and lower bounds and computing times.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.1
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• pp.1-10
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• 1995

The purpose of this paper is to develop a method of the sensitivity analysis that can be applied to a non-tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1a is the well known method applicable to a tree solution. However this method can not be applied to a non-tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient we present a method that the sensitivity analysis of Type 2 is solved by finding the shortest path. Besides we also show that the results of Type 2 and Type 1 are the same in a spanning tree solution. For the right-hand side constant or the capacity, the sensitivity analysis of Type 2 is solved by a simple calculation using arcs with intermediate values.

• Journal of the Korean Operations Research and Management Science Society
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• v.8 no.1
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• pp.19-26
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• 1983

This paper deals with the problem of locating facilities with upper and lower capacity bounds in a single level physical distribution system at minimum total costs. Several known schemes for location problems with upper capacity bounds only are successfully extended to our case and then implemented into our branch ana bound solution procedure. Computational experiments with twelve test problems suggest the effectiveness of our approach by showing that only a small amount of additional computation is required for our problem as compared to that for the problems with upper capacity bounds.

• International Journal of Control, Automation, and Systems
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• v.6 no.5
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• pp.776-784
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• 2008

In this paper, new upper matrix bounds for the solution of the continuous algebraic Riccati equation (CARE) are derived. Following the derivation of each bound, iterative algorithms are developed for obtaining sharper solution estimates. These bounds improve the restriction of the results proposed in a previous paper, and are more general. The proposed bounds are always calculated if the stabilizing solution of the CARE exists. Finally, numerical examples are given to demonstrate the effectiveness of the present schemes.

• IE interfaces
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• v.7 no.3
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• pp.193-199
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• 1994

The purpose of this paper is to develop a method of the sensitivity analysis that can be applicable to a degenerate tree solution of the minimum cost flow problem. First, we introduce two types of sensitivity analysis. A sensitivity analysis of Type 1 is the well known method applicable to a spanning tree solution. However, this method have some difficulties in case of being applied to a degenerate tree solution. So we propose a sensitivity analysis of Type 2 that keeps solutions of upper bounds remaining at upper bounds, those of lower bounds at lower bounds, and those of intermediate values at intermediate values. For the cost coefficient, we present a method that the sensitivity analysis of Type 2 is solved by using the method of a sensitivity analysis of Type 1. Besides we also show that the results of sensitivity analysis of Type 2 are union set of those of Type 1 sensitivity analysis. For the right-hand side constant or the capacity, we present a simple method for the sensitivity analysis of Type 2 which uses arcs with intermediate values.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.3
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• pp.171-180
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• 1992

This paper proposes a solution approach to linear problems with many constraints of variable upper bound (VUB) type. This type of constraints are commonly found in various scheduling type problems for which tighter bounds are essential to achieve an efficiency in enumeration. An analytical framework based on factorization is adopted to devise a solution approach to the problem and extend it for more generalized VUB problem (GVUB). This research shows why the VUB type constraints are amenable to the factorization and gives a unified approach to generalized upper bound(GUB) problems, VUB problems and GVUB problems. Implementation issues are also included.

• International Journal of Control, Automation, and Systems
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• v.1 no.4
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• pp.459-463
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• 2003

In this paper, new results using bounds for the solution of the discrete Lyapunov matrix equation are proposed, and some of the existing works are generalized. The bounds obtained are advantageous in that they provide nontrivial upper bounds even when some existing results yield trivial ones.

• 제어로봇시스템학회:학술대회논문집
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• 1986.10a
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• pp.68-72
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• 1986

Upper bounds of the perturbed Co-semigroups of the infinite dimensional systems are investigated by using the algebraic Riccati equation(ARE). In the case that the solution P of the ARE is strictly positive, the perturbed semigroups are uniformly bounded. A sufficient condition for the solution P to be strictly positive is provided. The uniform boundedness plays an important role in extending approximately weak stability to weak stability on th whole space. Exponential Stability of the perturbed semigroups is studied by using the Young's inequlity. Some further discussions on the uniform boundedness of the perturbed semigroups are given.