• 대한전기학회논문지:전력기술부문A
• /
• 제48권10호
• /
• pp.1207-1214
• /
• 1999

Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 2000년도 추계학술대회 논문집 학회본부 A
• /
• pp.125-128
• /
• 2000

This paper presents an energy function which provides the direct relationships between the system stability and parameters of the exciter system. The energy function is derived from the energy conservation law by using the first motion integral. he time derivative does not absolutely satisfy the seminegativeness. However dE/dt usually has big negative value just after the fault clearing so that the energy is rapidly decreased. In this situation, the system state can be obviously confined in a stable region if the intial energy is less than the UEP energy. With these observation, two theorems are developed regarding the state confinement and asymptotic stability. Based on two theorems a new approximated direct energy method is developed to analyze the transient stability with the consideration of the exciter control effects. The proposed method has been tested for a single-machine-infinite bus system.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1998년도 추계학술대회 논문집 학회본부A
• /
• pp.263-268
• /
• 1998

Many papers have recently been presented to develop energy functions for power systems. However, earlier studies adopted case-by-case approaches, which failed to give a general approach to deal with various kinds of generator models. In this paper, two useful theorems are developed regarding the integral relationships of the generator power versus its phasor current and voltage. By using the proposed theorems, an exact energy conservation law can be derived from the complex integral. The proposed energy conservation law, which is free of the generator model, can be utilized to develop energy functions for various kinds of generator models including the speed governors, and exciters. An illustrative example is given for a multimachine system with the Eq' model of generator. This thesis also shows a possibility of more accurate and fast stability analysis by using the proposed Energy Conservation Law.

• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.485-493
• /
• 2005

A variety of Feynman's operational calculus for noncommuting operators was studied [2,3,4,5,6]. And a stability in the measures for Feynman's operational calculus was studied [9]. In this paper, we investigate a stability of the Feynman's operational calculus with respect to the operators.

• 대한전자공학회:학술대회논문집
• /
• 대한전자공학회 2003년도 하계종합학술대회 논문집 V
• /
• pp.2863-2866
• /
• 2003

In nonlinear control fields, for irregular nonlinear systems, control form which consists of approximate tracking control law and exact tracking control law and which switches between two laws has been proposed recently. In this thesis, we design new switching control law which connect approximate linearization control law and exact linearization control law by fuzzy rules for irregular nonlinear system, ball and beam system. Fuzzy switching controller designed by fuzzy concept is proved that designed scheme overcomes singularities of irregular system, improves unstability problem of switching procedure, and has more efficient control value through simulation. Stability of fuzzy control system proved by Lyapunov's stability theorems.

• 대한수학회논문집
• /
• 제17권1호
• /
• pp.155-163
• /
• 2002

The purpose of this paper is to establish discrete versions of the well-known Lyapunov's stability theorem and LaSalle's invariance theorem for a non-autonomous discrete dynamical system. Our proofs for these theorems are constructive in the sense that they are made by explicitly building a Lyapunov function for the system. A comparison between non-autonomous discrete dynamical systems and continuous dynamical systems is conducted.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제24권2호
• /
• pp.99-107
• /
• 2017

Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the definition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the definition of biderivations and the statements of the results in [14], and prove the corrected theorems.

• 대한수학회논문집
• /
• 제32권4호
• /
• pp.1009-1024
• /
• 2017

In this paper, we consider the new faster iterative scheme due to Sintunavarat and Pitea ([32]) for further investigation and we prove its strong and ${\Delta}$-convergence theorems, data dependence and stability results in hyperbolic space. Our results extend, improve and generalize several recent results in CAT(0) space and uniformly convex Banach space.

• 대한전자공학회논문지
• /
• 제25권12호
• /
• pp.1610-1617
• /
• 1988

In this paper, a robust discrete-time adaptive control with compensation is proposed for single-input single-output discrete-time plants which have unmodeled dynamics. The stability of the overall system is studied using the conic sector stability theorems when a normalized constant gain parameter adaptation algorithm and a properly chosen compensation are used. An illustrative exmple shows that this compensation can also increase the parameter adaptation speed. And a method of compensation using the adaptive observation is also discussed.

• Korean Journal of Mathematics
• /
• 제31권3호
• /
• pp.269-294
• /
• 2023

The purpose of this paper is to introduce a new three-step iterative process and show that our iteration scheme is faster than other existing iteration schemes in the literature. We provide a numerical example supported by graphs and tables to validate our proofs. We also prove convergence and stability results for the approximation of fixed points of the contractive-like mapping in the framework of uniformly convex Banach space. In addition, we have established some weak and strong convergence theorems for nonexpansive mappings.