• Journal of Advanced Marine Engineering and Technology
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• v.28 no.8
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• pp.1299-1312
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• 2004

This paper suggests the simple form of a fuzzy PID controller and describes the design principle, tracking performance, stability analysis and changes of parameters of a suggested fuzzy PID controller. A fuzzy PID controller is derived from the design procedure of fuzzy control. It is well known that a fuzzy PID controller has a simple structure of the conventional PID controller but posses its self-tuning control capability and the gains of a fuzzy PID controller become nonlinear functions of the inputs. Nonlinear calculation during fuzzification, defuzzification and the fuzzy inference require more time in computation. To increase the applicability of a fuzzy PID controller to digital computer, a simple form of a fuzzy PID controller is introduced by the backward difference mapping and the analysis of the fuzzy input space. To guarantee the BIBO stability of a suggested fuzzy PID controller, ‘small gain theorem’ which proves the BIBO stability of a fuzzy PI and a fuzzy PD controller is used. After a detailed stability analysis using ‘small gain theorem’, from which a simple and practical method to decide the parameters of a fuzzy PID controller is derived. Through the computer simulations for the linear and nonlinear plants, the performance of a suggested fuzzy PID controller will be assured and the variation of the gains of a fuzzy PID controller will be investigated.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.515-536
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• 2012

This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is first established to obtain the moment stability but without almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while existing Razumikhin-type theorems aim at only the moment stability. By virtue of the $M$-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.19 no.6
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• pp.61-66
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• 2020

For simple and repetitive transport tasks in limited spaces such as in factories, it is more efficient to use mobile robots instead of human workers. For this reason, the reliance on mobile robots is increasing due to the increased implementation of smart factories. Currently, the structural design of the Mecanum wheel is required to ensure the stability of the moving robot since it is used for the transport of not only small products but also large products. In this paper, to improve the stability and durability of the Mecanum wheel, ways to improve the structure of the Mecanum wheel are presented. Then, using the Castigliano theorem, the structural stability is reviewed through the deflection on existing and improved structures.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.1
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• pp.1-7
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• 2001

For a parametric uncertain system, there are many results on stability analysis, but only a few synthesis methods. In this paper, we proposed a new target polynomial decision method for the parametric uncertain system to stabilize the closed loop system with maximal parametric $l_2$ stability margin. To this, we used both Lipatov Theorem and coefficient diagram method(CDM). To show the effectiveness of the proposed method, we designed a robust controller for the inverted pendulum system with parametric uncertainties using fixed order pole assignment(FOPA) method and its performance was compared with that of the ${\mu}$ synthesis methods.

• Bulletin of the Korean Mathematical Society
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• v.49 no.5
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• pp.899-910
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• 2012

Let $\mathcal{H}$ be a complex separable infinite dimensional Hilbert space. In this paper, a necessary and sufficient condition is given for an operator T on $\mathcal{H}$ to satisfy that $f(T)$ obeys generalized Weyl's theorem for each function $f$ analytic on some neighborhood of ${\sigma}(T)$. Also we investigate the stability of generalized Weyl's theorem under (small) compact perturbations.

• 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.8 no.2
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• pp.581-590
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• 2001

In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

• Kyungpook Mathematical Journal
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• v.56 no.2
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• pp.431-450
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• 2016

In this paper, the existence, uniqueness, stability via continuous dependence and Ulam stabilities of nonlinear integro-differential equations with random impulses are studied under sufficient condition. The results are obtained by using Leray-Schauder alternative fixed point theorem and Banach contraction principle.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.889-901
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• 1998

Numerical approximations by pseudospectral method are obtained for the damped Boussinesq equation which is a modification of the good Boussinesq equation. The consistency and stability of the method are obtained using the extended Lax-Richtmyer equivalence theorem, which imply the convergence of the method. We obtain error estimates of O(h$^{s}$ ＋ k$^2$) for a fully discrete pseudospectral method.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.283-286
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• 1995

Due to finite bandwidth of missile dynamics, guidance commands in PN guidance tend to diverage as the missile approaches to the target. In this paper, a new method based on the short-time stability theorem is introduced to extend the stability region.