• Journal of Advanced Navigation Technology
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• v.23 no.6
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• pp.577-583
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• 2019

A dynamic system is called positive if any trajectory of the system starting from non-negative initial states remains forever non-negative for non-negative controls. In this paper, we consider the new stability condition for the positive time-varying linear discrete interval systems with time-varying delay and unstructured uncertainty. The delay time is considered as time-varying within certain interval having minimum and maximum values and the system is subjected to nonlinear unstructured uncertainty which only gives information on uncertainty magnitude. The proposed stability condition is an improvement of the previous results which can be applied only to time-invariant systems or had no consideration of uncertainty, and they can be expressed in the form of a very simple inequality. The stability conditions are derived using the Lyapunov stability theory and have many advantages over previous results using the upper solution bound of the Lyapunov equation. Through numerical example, the proposed stability conditions are proven to be effective and can include the existing results.

• Journal of the Korea institute for structural maintenance and inspection
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• v.14 no.4
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• pp.55-61
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• 2010

This paper is concerned with an experimental research to random vibration control caused by external loads specially in bridges which tend to be structurally flexible. Experimenting on a reduced structure modelled on Seohae Grand Bridge, we inflicted a reduced form of El-centro wave on the model structure to a proper proportion. On the center of its middle span, we placed a shear type MR damper which was to control its vibration and also acquire its structural responses such as displacement and acceleration at the same site. The experiments concerning controlling vibration were performed according to a variety of theories including un-control, passive on/off control, and Lyapunov stability theory. Its control performance was evaluated in terms of the peak absolute displacements, the peak absolute accelerations and the total power required to control the bridge which differ from each different experiment method. Among all the methods applied in this paper, case of Lyapunov control method turned out to be the most effective to reduces of displacement and acceleration. Also, this method could to decrease consuming of external power for vibration control. Finally, it was noteworthy that Lyapunov control method was specially effective in the vibration control employing a semi-active damper such MR damper.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.486-491
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• 1999

본 논문에서는 웨이브렛 신경회로망을 사용하여 알려지지 않은 비선형 시스템을 안정하게 적응 제어하는 문제를 다룬다. 비선형 시스템의 정확한 제어는 함수를 근사화하는 데 사용된 함수 근사화기의 정확성과 효율성에 의존한다. 이에 비선형 시스템 제어에 기준 함수의 선택이 자유롭고 함수 근사화 능력이 뛰어난 웨이브렛 신경회로망을 사용한다. 초기 웨이브렛 신경회로망 제어기 설정은 웨이브렛 신경회로망 변수인 신축과 이동 값을 제어기 입력의 시-주파수 특성을 분석해서 구하고, 연결강도는 Lyapunov 안정성 이론에 기초한 적응 법칙을 사용하여 조절한다. 이를 비선형 시스템인 역 진자 시스템에 적용한다.

• 제어로봇시스템학회:학술대회논문집
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• 1987.10b
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• pp.130-134
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• 1987

이 논문에서는 매개변수(parameter)들이 시간에 따라 변하는 선형 시변 시스템(linear time-varying system)에서 시스템의 안정도(stability)를 보장할 수 있는 매개변수들의 변동영역(perturbation region of parameters)에 대한 충분조건을 시간영역에서 Lyapunov 방법을 사용하여 구하였다. 그리고 이 충분조건을 만족하는 매개변수 변동영역을 비선형 계획법(nonlinear programing)을 이용하여 구하는 방법을 제시하였다. 시뮬레이션 결과 이 방법으로 지금까지 이루어져 왔던 다른 연구 결과들보다 더 넓고 다양한 매개변수 변동영역을 구할 수 있었다.

• Journal of Korea Society of Industrial Information Systems
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• v.9 no.4
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• pp.75-79
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• 2004

We investigate various $\phi_0-boundedness$ and $\phi_0-Lagrange$ stability of the trivial solution of comparison differential system. We also investigated the corresponding boundedness concepts of the trivial solution of the differential system using the theory of differential inequalities through cones and the method of cone valued Lyapunov functions.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.210-213
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• 1988

By using Lyapunov method, sufficient conditions for linear time-varying continuous-time and discrete-time systems to be stable are presented under the assumption that the systems are slowly time-varying. Though it is not simple to find the stability regions immediately, one could find practical and large stability regions by constructing an appropriate algorithm.

• Journal of IKEEE
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• v.23 no.4
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• pp.1265-1272
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• 2019

We analyze the robustness of the existing predictor feedback controller for discrete-time linear systems with constant input delays against the structured model uncertainty. By modeling the constant input delay with a first-order PdE (Partial difference Equation), we replace the input delay with the PdE states. By applying a backstepping transformation, we build a target system that enables to construct an explicit Lyapunov function. Constructing the explicit Lyapunov function that covers the entire state variables, we prove the existence of an allowable maximum size of the structured model uncertainty to maintain stability and establish the robustness of the predictor feedback controller. The numerical example demonstrates that the stability of closed-loop system is maintained in the presence of the structured model uncertainty, and verifies the robustness of the predictor feedback controller.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.36 no.10
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• pp.1147-1154
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• 2012

In this study, a method for designing blade pitch and generator torque controllers for a wind turbine generator is presented. This method consists of two steps. First, the Lyapunov stability theory is used to obtain nonlinear control laws that can regulate the rotor speed and the power output at all operating ranges. The blade pitch controller is chosen such that it always decreases a positive definite function that represents the error in rotor speed control. Similarly, the generator torque controller always decreases a positive definite function that reflects the error in power output control. Then, the simulation-based optimization technique is used to tune the design parameters. The controller design procedure and simulation results are presented using the widely adopted two-mass model of the wind turbine.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.40 no.7
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• pp.574-581
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• 2012

Because of the exposed blade, the UAV using the rotors entail the risks during operation. While a wrapped duct around the fan blades reduces risks, it is a higher thrust performance than the same power load rotor. In this paper, for applying advantages of a ducted fan, the tri-ducted fan air vehicle configuration is proposed. The vehicle has three ducted fans. Two of them are the same shape and size and the third one is the smaller. It is possible to control a rapid attitude stability using thrust vector control. The equations of motion of the tri-ducted fan were derived. Lyapunov control input was applied to the system and stable inputs were derived. A nonlinear simulation was fulfilled by using parameters of a prototype vehicle. It verified a stable attitude and analyzed results.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.476-482
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• 2010

In this paper, we propose a robust path tracking control method for autonomous underwater vehicle with variable speed. The proposed path tracking controller consists of a kinematic controller and a dynamic controller. First, the kinematic controller computes the surge speed and yaw rate to follow the reference path with variable speed. Then the dynamic controller controls the thrust force and yaw torque to move the AUV actually. In the dynamic control, we assume that the sway speed is a disturbance. In addition the dynamic controller is designed based on sliding mode conrol. We also demonstrate the stability of the proposed control method by Lyapunov stability theory. Finally, simulation results illustrate the performance of the proposed control method.