• Journal of applied mathematics & informatics
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• 제23권1_2호
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• pp.345-352
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• 2007

In this paper, cone-valued Lyapunov functions are employed to study the impulsive control system with variable times. The stability criteria on the non-zero solution of the impulsive control system are given by the cone-valued Lyapunov functions and the results of the controllability on the control system are also obtained.

• 한국음향학회지
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• 제16권4호
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• pp.42-48
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• 1997

본 논문에서는 음성을 비선형 결정론적 발생메카니즘에서 발생되는 불규칙한 신호인 카오스로 보고 상관차원과 Lyapunov 차원을 구함으로써 음성화자식별 파라미터와 음성인식파라미터에 대한 성능을 평가하였다. Taken의 매립정리를 이용하여 스트레인지 어트렉터를 구성할 때 AR모델의 파워스펙트럼으로부터 주요주기를 구함으로써 정확한 상관차원과 Lyapunov 차원을 추정하였다. 이트렉터 궤도의 특징을 잘 나타내는 상관차원과 Lyapunov 차원을 가지고 음성인식과 화자인식의 특징파라미터로의 효용성을 고찰하였다. 그 결과, 음성인식보다는 화자식별의 특징파라미터로타당하였으며 화자식별 특징파라미터로서는 상관차원보다는 Lyapunov 차원이 높은 화자식별 인식율을 얻을 수 있음을 알았다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2006년 학술대회 논문집 정보 및 제어부문
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• pp.324-326
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• 2006

This paper present backstepping control approach for controling chaotic Liu system. The proposed method is a systematic design approach and consists in a recursive procedure that interlaces the choice of a Lyapunov Function. Based on Lyapunov stability theory, control laws are derived. We used the same technique to enable stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory to be achieved in a systematic way. Numerical solution are shown to verify the result.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.334-334
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• 2000

In this paper, sliding mode observer design principles based on the equivalent control approach are discussed for the systems which may not satisfy the matching conditions. We propose a new approach for designing a sliding observer and the proof of the stability of the state reconstruction error system for time-invariant systems using the Lyapunov method. The reaching time to the sliding surface, the sliding dynamics of the system, the stability of the reconstruction error system via Lyapunov method, sufficient conditions for the existence of the sliding mode are studied.

• 제어로봇시스템학회논문지
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• 제20권3호
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• pp.261-269
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• 2014

This paper provides an overview of the basics and recent studies of Lyapunov-based nonlinear adaptive control, the aim of which is to improve or maintain the performance and stability of the closed-loop system by cancelling out the presumable uncertainties in the nonlinear system dynamics. The design principles are essentially based on Lyapunov's direct method. In this survey, we provide a comprehensive overview of Lyapunov-based nonlinear adaptive control techniques with simplified effective design examples, which are to be elaborated as related recent results are gradually shown. The scope of the survey contains research on singularity problems in adaptive control, the techniques to deal with linearly and nonlinearly parameterized uncertainties, robust neuro-adaptive control, and adaptive control methodologies combined with various nonlinear control techniques such as sliding-mode control, back-stepping, dynamic surface control, and optimal/$H_{\infty}$ control.

• 제어로봇시스템학회논문지
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• 제8권2호
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• pp.167-177
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• 2002

In Strapdown Inertial Navigation System(SDINS), error models based on previously proposed conversion equations between the attitude errors, are only valid in case the attitude errors are small. The SDINS error models have been independently studied according to the definition of the reference frame and of the attitude error. The conversion equations between the attitude errors applicable to SDINS with large attitude errors are newly derived. Lyapunov transformation matrices are also derived from the obtained results. Furthermore the general method, which is independent of the attitude error and the reference frame to derive SDINS error model, is proposed using the Lyapunov transformation.

• 제어로봇시스템학회논문지
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• 제12권5호
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• pp.411-418
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• 2006

There are mainly two types of bang-bang controllers for nominal linear time-invariant (LTI) system. Optimal bang-bang controller is designed based on optimal control theory and suboptimal bang-bang controller is obtained by using Lyapunov stability condition. In this paper, the suboptimal bang-bang control method is extended to LTI system involving both control input saturation and structured real parameter uncertainties by using Lyapunov robust stability condition. Two robust optimal bang-bang controllers are derived by minimizing the time derivative of Lyapunov function subjected to the limit of control input. The one is developed based on the classical quadratic stability(QS), and the other is developed based on the affine quadratic stability(AQS). And characteristics of the two controllers are compared. Especially, bounds of parameter uncertainties which theoretically guarantee robust stability of the two controllers are compared quantitatively for 1DOF vibrating system. Moreover, the validity of robust optimal bang-bang controller based on the AQS is shown through numerical simulations for this system.

• Journal of the Korean Data and Information Science Society
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• 제21권3호
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• pp.597-603
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• 2010

We obtain, in using generalized norms, some stability results for a very general system of di erential equations using the method of cone-valued Lyapunov funtions and we obtain necessary and/or sufficient conditions for the uniformly asymptotic stability of the nonlinear differential system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1994년도 Proceedings of the Korea Automatic Control Conference, 9th (KACC) ; Taejeon, Korea; 17-20 Oct. 1994
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• pp.543-547
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• 1994

In this paper, the new approach and technique are introduced and derived from the original Lyapunov direct method which is used to decide the stability of system conveniently. This proposed technique modifies the formal concepts of the sufficient conditions of Lyapunov stability and is able to generate the methods for the robust design of control systems. Also, it applies to the dynamic systems with bounded perturbations and the results of the computer program using the new concept are compared with those of previous research papers and conventional Lyapunov direct method. It is possible to recognize the practical improvements of the estimation of robustness bounds of the systems.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권4호
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• pp.329-336
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• 2011

Some new Lyapunov-type inequalities for a class of nonlinear differential systems, which are natural refinements and generalizations of the well-known Lyapunov inequality for linear second order differential equations, are given. The results of this paper cover some previous results on this topic.