• Journal of the Korea Society of Computer and Information
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• v.18 no.6
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• pp.9-19
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• 2013

This paper deals with fuzzy $H_{\infty}$ filtering problem of discrete-time nonlinear Markovian jump systems with state and output time delays. The purpose is to design fuzzy $H_{\infty}$ filter such that the corresponding estimation error system with time delays and initial state uncertainties is stochastically stable and satisfies an $H_{\infty}$ performance level. A sufficient condition for the existence of fuzzy $H_{\infty}$ filter is given in terms of matrix inequalities. In order to relax conservatism, a stochastic mode dependent fuzzy Lyapunov function is employed. The Lyapunov function not only is dependent on the operation modes of system, but also includes the fuzzy membership functions. An illustrative example is finally given to show the applicability and effectiveness of the proposed method.

• 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 Institute of Electronics Engineers of Korea SC
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• v.37 no.6
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• pp.7-14
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• 2000

This paper describes the synthesis of robust decentralized controllers for uncertain large-scale discrete-time systems with time-delays in subsystem interconnections. Based on the Lyapunov method, a sufficient condition for robust stability, is derived in terms of a linear matrix inequality (LMI). The solutions of the LMI can be easily obtained using various efficient convex optimization techniques. A numerical example is given to illustrate the proposed method.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.37 no.6
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• pp.1-6
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• 2000

In this paper, the problem of the stability analysis for linear neutral delay-differential systems with nonlinear perturbations is investigated. Using Lyapunov second method, a new delay-dependent sufficient condition for asymptotic stability of the systems in terms of linear matrix inequalities (LMIs), which can be easily solved by various convex optimization algorithms, is presented. A numerical example is given to illustrate the proposed method.

• The Journal of the Korea institute of electronic communication sciences
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• v.13 no.1
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• pp.93-100
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• 2018

This study proposes a controller that compensates torque error for precise angular velocity tracking and a method to compensate the stability of controller in implementation. Also, it is proved that the designed controller can be asymptotically stable based on Lyapunov stability theory. The proposed controller is able to control the d-axis reference current to arbitrary values and easily achieve control performance with two gains. As a result of applying to IPMSM of about 750W class, the steady state error with reference speed 1200 [RPM] is within 0.1 [%]. And it can be seen that it is an asymptomatic stable controller overcoming disturbance within about 0.2 second in application of constant load of about 5 [Nm].

• Proceedings of the Korea Information Processing Society Conference
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• 2017.11a
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• pp.75-77
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• 2017

디지털 제어와 사물 인터넷을 통한 네트워크 기반 제어가 확산되면서 정밀 제어를 위한 양자화 오류에 대한 고려의 중요성이 증가하고 있다. 본 연구에서는 이산 시간 출력 궤환 제어 시스템에서 제어 신호 생성에 사용되는 시스템 출력 신호에 양자화 오류가 있을 때, 리아푸노프 시스템 안정성을 보장하는 조건을 선형 행렬 부등식을 통하여 제시한다.

• Journal of Advanced Navigation Technology
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• v.25 no.6
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• pp.551-556
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• 2021

In this paper, we deal with the stability condition of linear interval discrete systems with time-varying delays and unstructured uncertainty. For the interval discrete system which has interval matrix as its system matrices, time-varying delay time within some interval value and unstructured uncertainty which can include non-linearity and be expressed by only its magnitude, the stability condition is proposed. Compared with the previous result derived by using a upper bound solution of the Lyapunov equation, the new results are derived by the form of simple inequality based on Lyapunov stability condition and have the advantage of being more effective in stability application. Furthermore, the proposed stable conditions are very comprehensive and powerful, including the previously published stable conditions of various linear discrete systems. The superiority of the new condition is proven in the derivation process, and the utility and superiority of the proposed condition are examined through numerical example.

• Journal of Advanced Navigation Technology
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• v.26 no.6
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• pp.504-509
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• 2022

In this paper, we deal with the stability condition of linear time-varying interval discrete systems with time-varying delays and unstructured uncertainty. For the time-varying interval discrete system which has interval matrix as its system matrices, time-varying delay time within some interval value and unstructured uncertainty which can include non-linearity and be expressed by only its magnitude, the stability condition is proposed. Compared with the previous result derived by using a upper bound solution of the Lyapunov equation, the new result is derived by the form of simple inequality based on Lyapunov stability condition and has the advantage of being more effective in checking stability. Furthermore, the proposed condition is very comprehensive, powerful and inclusive the previously published conditions of various linear discrete systems, and can be expressed by the terms of magnitudes of the time-varying delay time and uncertainty, and bounds of interval matrices. The superiority of the new condition is shown in the derivation, and the usefulness and advantage of the proposed condition are examined through numerical example.

• Journal of Advanced Navigation Technology
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• v.20 no.5
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• pp.475-481
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• 2016

In this paper, the new stability condition of linear discrete interval time-varying systems with time-varying delay time is proposed. The considered system has interval time-varying system matrices for both non-delayed and delayed states with time-varying delay time within given interval values. The proposed condition is derived by using Lyapunov stability theory and expressed by very simple inequality. The restricted stability issue on the interval time-invariant system is expanded to interval time-varying system and a powerful stability condition which is more comprehensive than the previous is proposed. As a results, it is possible to avoid the introduction of complex linear matrix inequality (LMI) or upper solution bound of Lyapunov equation in the derivation of sufficient condition. Also, it is shown that the proposed result can include the many existing stability conditions in the previous literatures. A numerical example in the pe revious works is modified to more general interval system and shows the expandability and effectiveness of the new stability condition.

• 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.