• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.3
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• pp.73-78
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• 2001

This paper presents sliding mode control(SMC) method using target variation rate of Lyapunov Function. SMC keeps the response of structure in sliding surface where structure is stable. It can design both linear controller and bang-bang controller. Linear control of previous research, however, can not make most of the performance of controller, because it is designed to satisfy the condition that the variation rate of Lyapunov function is minus. Also, in case of bang-bang controller, unnecessary large control force is generated. Presented method can utilize the capacity of controller efficiently by prescribing the target variation rate of Lyapunov function. Numerical simulation results indicate that the presented control methods can reduce the peak response larger than linear control, and it has control performance equivalent to bang-bang control.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.459-459
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• 2000

The purpose of this paper is the application of the techniques for the new estimation of robustness for the aircraft systems having structured uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. The number of uncertainties will be the degree of freedoms in the calculation of the robust stability regions called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, in this paper, the quadratic form of Lyapunov function is utilized. In this paper, the practical system of vertical take-off and landing (VTOL) aircraft is analyzed with the proposed stability criteria based upon the Lyapunov direct method. The application of numerical procedures can prove the improvements in estimations of robustness with structured uncertainties. The applicable aircraft system is assumed to be linear with time-varying with nonlinear bounded perturbations.

• Proceedings of the Earthquake Engineering Society of Korea Conference
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• 2001.04a
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• pp.163-171
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• 2001

This paper presents sliding mode control(SMC) method using target variation rate of Lypunov Function. SMC keeps the response of structure in sliding surface where structure is stable. It can design both linear controller and bang-bang controller. Linear control of previous research, however, can not make most of the performance of controller, because it is designed to satisfy the condition that the variation rate of Lyapunov function is minus. Also, incase of bang-bang controller, unnecessary large control force is generated. Presented method can utilize the capacity of controller efficiently by prescribing the target variation rate of Lyapunov function. Numerical simulation results indicate that the presented control methods can reduce the peak response larger than linear control, and it has control performance equivalent to bang-bang control.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.20-22
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• 2005

In this paper, we propose a novel stability criterion for switched linear systems. The proposed method employs the results on the upper bound of the solution of LME(Lyapunov Matrix Equation) and on the stability of hybrid system. The former guarantees the existence of Lyapunov-like energy functions and the latter shows that the stability of switched linear systems by using these energy functions. The proposed criterion releases the restriction on the stability of switched linear systems comparing with the existing methods and provides us with easy implementation way for pole assignment.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1647-1652
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2009.05a
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• pp.171-174
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• 2009

Generally the neural network and the fuzzy compensative algorithm are applied to forecast the time series for power demand with a characteristic of non-linear dynamic system, but it has a few prediction errors relatively. It also makes long term forecast difficult for sensitivity on the initial condition. On this paper, we evaluate the chaotic characteristic of electrical power demand with analysis methods of qualitative and quantitative and perform a forecast simulation of electrical power demand in regular sequence, attractor reconstruction, time series forecast for multi dimension using Lyapunov exponent quantitatively. We compare simulated results with the previous method and verify that the purpose one being more practice and effective than it.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.700-705
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• 2005

The purpose of this project is the derivation and development of techniques for the new estimation of robustness for the systems having uncertainties. The basic ideas to analyze the system which is the originally nonlinear is Lyapunov direct theorems. The nonlinear systems have various forms of terms inside the system equations and this investigation is confined in the form of bounded uncertainties. Bounded means the uncertainties are with same positive/negative range. The number of uncertainties will be the degree of freedoms in the calculation of the stability region. This is so called the robustness bounds. This proposition adopts the theoretical analysis of the Lyapunov direct methods, that is, the sign properties of the Lyapunov function derivative integrated along finite intervals of time, in place of the original method of the sign properties of the time derivative of the Lyapunov function itself. This is the new sufficient criteria to relax the stability condition and is used to generate techniques for the robust design of control systems with structured perturbations. Using this relaxing stability conditions, the selection of Lyapunov candidate function is of various forms. In this paper, the quadratic form is selected. this generated techniques has been demonstrated by recent research interest in the area of robust control design and confirms that estimation of robustness bounds will be improved upon those obtained by results of the original Lyapunov method. In this paper, the symbolic algebraic procedures are utilized and the calculating errors are reduced in the numerical procedures. The application of numerical procedures can prove the improvements in estimations of robustness for one-and more structured perturbations. The applicable systems is assumed to be linear with time-varying with nonlinear bounded perturbations. This new techniques will be extended to other nonlinear systems with various forms of uncertainties, especially in the nonlinear case of the unstructured perturbations and also with various control method.

• Annals of Clinical Neurophysiology
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• v.8 no.2
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• pp.135-145
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• 2006

Background: Parkinson's disease is movement disorder due to dopaminergic deficiency. It has been noted that cognitive dysfunction also presented on Parkinson's disease patients. But, it is not clear whether such a cognitive dysfunction was a dopaminergic dysfunction or cholinergic dysfunction. Using linear and non-linear analyses, we analysed the effect of cognitive and motor symptom on EEG change. Methods: EEGs were recorded from patients with Parkinson's disease and essential tremor, and normal controls during rest. We calculated the power spectrum, correlation dimension and Lyapunov exponent by using 'Complexity'program. The power spectrum, correlation dimension, and Lyapunov exponent were compared between Parkinson's disease patients and essential tremor patients. Results: Theta power was increased in Parkinson's disease patient group. Correlation dimension was increased in Parkinson's disease patients. Positive correlation was noted between MMSE and correlation dimension, and negative correlation was noted between MMSE and Lyapunov exponent. Lyapunov exponent was decreased in Parkinson's disease patient. Conclusions: We conclude that the state of Parkinson's disease patient is characterized by increased correlation dimension and decreased Lyapunov exponent.

• Journal of the Korean Institute of Telematics and Electronics
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• v.11 no.4
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• pp.5-8
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• 1974

In this paper, several criterias of Lyapunov, Malkin, Popov, etc. about stability of nonlinear systems are compared, and study on methods, through several examples, of judging the stability of nonlinear systems by considering the energy input into the system and the one put out of the system is concentrated.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.39-42
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• 2002

This paper focuses on the asymptotic stability of a class of neutral linear systems with mixed time-varying delay arguments. Using the Lyapunov method, a delay-dependent stability criterion to guarantee the asymptotic stability for the systems is derived in terms of linear matrix inequalities (LMIs). The LMIs can be easily solved by various convex optimization algorithms. Two numerical examples are given to illustrate the proposed methods.