• Structural Engineering and Mechanics
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• v.5 no.5
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• pp.577-586
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• 1997

In nonlinear finite element stability analysis of structures, the foremost necessary procedure is the computation to precisely locate a singular equilibrium point, at which the instability occurs. The present study describes global and local procedures for the computation of stability points including bifurcation points and limit points. The starting point, at which the procedure will be initiated, may be close to or arbitrarily far away from the target point. It may also be an equilibrium point or non-equilibrium point. Apart from the usual equilibrium path, bypass and homotopy path are proposed as the global path to the stability point. A local iterative method is necessary, when it is inspected that the computed path point is sufficiently close to the stability point.

• Journal of the Korean Statistical Society
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• v.32 no.4
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• pp.337-357
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• 2003

This paper introduces new measures for the stability of slope estimation on the second order response surface at a point and on a sphere. As a measure of point stability of slope estimation, we suggest a point dispersion measure of slope variances over all directions at a point. A spherical dispersion measure is also proposed as a measure of spherical stability of slope estimation on each sphere. Some designs are studied to explore the usefulness of the proposed measures. Using the point dispersion measure, another concept of slope rotatability called equally-stable slope rotatability is proposed as a useful property of response surface designs. We provide a set of conditions for a design to have equally-stable slope rotatability.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2001.04a
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• pp.574-577
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• 2001

This paper presents the comparison of FRI(Foot Rotation Indicator) point and ZMP(Zero Moment Point) in biped robot stability. We showed FRI may be employed as a useful tool in stability analysis in biped robot. Also, we proposed the balancing joint trajectory derived from FRI point equation for stable gait. The numerical calculation routines and walking algorithms for simulation are performed by MATLAB. The procedure is composed of the leg trajectory planning, the generation of balancing trajectory, and the verification of dynamic stability.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.345-351
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• 2005

An effective method for analyzing the stability of nonlinear systems is developed. After introducing a novel concept named the point- wise generalized Dahlquist constant for any mapping and presenting its useful properties, we show that the point-wise generalized Dahlquist constant is sufficient for characterizing the exponential stability of nonlinear systems.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.3
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• pp.238-243
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• 2009

This paper present same thodology for the classification of power system voltage stability, the trajectory of which to instability is monotonic, using an interior point method based support vector machine(IPMSVM). The SVM based voltage stability classifier canp rovide real-time stability identification only using the local measurement data, without the topological information conventionally used.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.671-684
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• 2023

In this paper, we prove the generalized Hyers-Ulam stability of a general quintic functional equation, $\sum\limits_{k=0}^{6}(-1)^k{_6}C_kf(x+(3-k)y)=0$, by using the fixed point method.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.51 no.11
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• pp.535-543
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• 2002

Modern power grids are becoming more and more stressed with the load demands increasing continually. Therefore large stressed power systems exhibit complicated dynamic behavior when subjected to small disturbance. Especially, it is needed to analyze special conditions which make small signal stability structure varied according to operating conditions. This paper shows that the relation between small signal stability structure varied according to operating conditions. This paper shows that the relation between small signal stability and operating conditions can be identified well using node-focus point and 1:1 resonance point. Also, the weak point which limits operating range is found by the analysis of resonance condition, and it is shown that reactive power compensation may solve the problem in the weak points. The proposed method is applied to test systems, and the results illustrate its capabilities.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.648-651
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• 2004

Biped robot has better mobility than other mobile robot, but it is hard to maintain balance during walking. In order to maintain balance, stability analysis is a key point for a biped robot. The zero moment point analysis has been used most in stability analysis. In this paper, we propose different method of stability analysis using wrench system. It is possible to generate a wrench system by applying a force along an axis in space and simultaneously applying a moment about the same axis. Wrench system is equivalent to a force and moment applied along the same axis. We compare the result of wrench system analysis with that of zero moment analysis in biped robot stability using simulation program.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.467-470
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• 1994

In this paper, we develop two sufficient conditions for Schur stability of convex combinations of discrete time polynomials. We give conditions under which Schur stability of the extremes implies Schur stability of the entire convex combination. These results are based on Bhattacharyya's result(1991), the AHMC theory in Barmish and Kang's paper (1993) and the bilinear transformation. Important applications of the results involves robust Schur stability of a feedback system having degenerate interval plants in an extreme point context.