• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.429-440
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• 1999

In this paper an electrochemistry model which consists of three charged species is considered. A dissociation-association reaction is allowed to take place between these species. The species of ions diffuse owing to concentration gradients and migrate because of electric forces. We prove that any initial distribution of species concentrations will settle down to the unique steady state as time becomes large.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.231-242
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• 2004

The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. Here we have studied dynamical model of a single-species population-toxicant system. Two cases are studied: constant exogeneous input of toxicant and rapidly fluctuating random exogeneous input of toxicant into the environment. The dynamical behaviour of the system is analyzed by using deterministic linearized technique, Lyapunov method and stochastic linearization on the assumption that exogeneous input of toxicant into the environment behaves like ‘Coloured noise’.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.583-596
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• 2010

In this paper, the problem of delay-dependent stability analysis for cellular neural networks systems with time-varying delays was considered. By using a new Lyapunov-Krasovskii function, delay-dependant stability conditions of the delayed cellular neural networks systems are proposed in terms of linear matrix inequalities (LMIs). Examples are provided to demonstrate the reduced conservatism of the proposed stability results.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.743-750
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• 2009

A class of Hermitian operators B admitting a positive semidefinite solution of the linear operator equation ${\sum}^n_{j=1}A^{n-j}XA^{j-1}=B$ for a fixed positive definite operator A is given via the Furuta inequality.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.12
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• pp.884-893
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• 1988

Adaptive controllers for linear unknown coefficient system, that is corrupted by disturbance, are designed by parameter adaptation model reference adaptive control(MRAC). This design is stemmed from the Lyapunov direct method. To reduce the model following error and to improve the convergence rate of the design, an indirect-suboptimal control law is derived. Proper compensation for the effects of time-varying coefficients and plant disturbance are suggested. In the design procedure no complete identification of unknown coefficients are required.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.169-174
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• 2005

A neural networks (NN) saturation compensation scheme for DC motor systems is presented. The scheme that leads to stability, command following and disturbance rejection is rigorously proved. On-line weights tuning law, the overall closed loop performance and the boundness of the NN weights are derived and guaranteed based on Lyapunov approach. The simulation and experimental results show that the proposed scheme effectively compensate for saturation nonlinearity in the presence of system uncertainty.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.3
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• pp.26-32
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• 1998

본 논문은 파라미터 불확실성을 가지는 비선형 시스템을 안정화하는 견실 퍼지 제어기 설계 기법을 제시한다. 견실 퍼지 제어기를 설계하기 위하여, 비선형 시스템을 Takagi-Sugeon(T-S)모델로 표현하고 퍼지 제어기는 병렬 분한 보상(PDC : parallel distributed compensation)의 개념을 이용한다. Lyapunov함수를 이용하여 파라미터 불확실성을 가지는 T-S퍼지 모델의 안정성을 논하고, 견실 퍼지 제어기가 존재할 충분조건을 선형 행렬 부등식(LMI " linear materix inequality)을 이용하여 나타낸다. 이러한 선형 행렬 부등식의 해들로부터 견실 퍼지 제어기를 직접적으로 구할 수 있다.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.373-376
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• 2008

본 논문은 퍼지 펄스 폭 변조 (Pulse-width-modulation: PWM) 시스템의 안정도에 대해 다루게 된다. 복잡성을 가진 비선형 시스템은 Takagi-Sugeno (T-S) 퍼지 모델에 의해 효율적으로 논의될 수 있다. 본 논문에서는 기존의 LTI 시스템에서 논의 되었던 PWM 제어기 설계 문제를 퍼지 시스템으로 확장시킴으로써 PWM 제어기에 대한 논의의 저변을 확대시키고자 한다. 또한, 리아푸노프 (Lyapunov) 안정도에 기반 한 안정도 증명을 통해 퍼지 PWM 시스템의 안정도를 분석하고자 한다.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.74-74
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• 2000

This paper presents a neural network controller for a rigid-link electrically-driven robot. The proposed controller is designed in conjunction with three neural networks approximating for complicated nonlinear functions. Particularly, the fact, different from conventional schemes, is that the neural network based current observer is used. Therefore, no accurate measurement of the actuator driving current is required. In the proposed controller-observer scheme, the derived weight update rule guarantees the stability of closed-loop system in the sense of Lyapunov. The effectiveness and performance of the proposed method are demonstrated through computer simulation.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.536-536
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• 2000

In this paper, we show based on Lyapunov theorem that the closed loop system with the constrained H$_{\infty}$ optimal controller is exponentially stable. Then the on-line feedback implementation of the constrained H$_{\infty}$ optimal control based on quadratic programs is proposed.