• International Journal of Control, Automation, and Systems
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• 제2권3호
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• pp.384-389
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• 2004

Recently a method of model reduction for discrete systems has been proposed in the literature based on a new impulse response Gramian. In this method, the system matrix$A_r$ of a reduced model is computed by approximating the reduced-order impulse response Gramian. The remaining matrices $b_r$ and $c_r$ are obtained so that various initial Markov parameters and time-moments of the original system are preserved in the reduced model. In this paper a different approach is presented based on the recursive relationship among the impulse response Gramians.

• 제어로봇시스템학회논문지
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• 제1권1호
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• pp.1-3
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• 1995

결합된 시변 상미분 방정식의 해외 점근적 성질에 관한 연구이다. 리아프노프 직접 방법에 의하면 평등 안정성(uniform stability)만 얻어졌을 경우이지만, 추가적으로 상태 벡터 중 일부가 0으로 점근적 수렴함을 보이는데 있다. 얻어진 결과는 특히 불변원리(invariance principle)가 성립하지 않는 시변 시스템에 유용하다.

• 대한전기학회논문지:시스템및제어부문D
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• 제52권7호
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• pp.418-423
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• 2003

In order to describe the upper bound of the uncertainties without any information of the structure, we assume that the upper bound is represented as a Fredholm integral equation of the first kind, that is, an integral of the product of a predefined kernel with an unknown influence function. Based on the improved Lyapunov function, we propose an adaptation law that is capable of estimating the upper bound and we design a sliding mode control, which controls effectively for uncertain dynamic systems.

• 대한전자공학회논문지
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• 제25권12호
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• pp.1625-1632
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• 1988

This paper aims not only to introduce the concept of linear singular systems, geometric structure, and feedback but also to provide applications of the multivariable linear singular system theories to electric circuits which may appear in some electronic equipments. The impulsive or discontinuous behavior which is not desirable can be removed by the set of admissible initial conditions. The output-nulling supremal (A,E,B) invariant subspace and the singular system structure algorithm are applied to this double-input double-output electric circuit. The Weierstrass form of the pencil (s E-A) is related to the output-nulling supremal (A,E,B) invariant subspace from which the time domain solutions of the finite and the infinite subsystems are found. The generalized Lyapunov equation for this application with feedback is studied and finally, the use of orthogonal functions in singular systems is discussed.

• 한국소음진동공학회논문집
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• 제14권7호
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• pp.561-568
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• 2004

The nonlinear dynamic characteristic of a straight tube conveying fluid with constraints and an attached mass on the tube is examined in this study An experimental apparatus with an elastomer tube conveying water which has an attached mass and constraints is made and comparisons are made between the theoretical results from the non-linear equation of motion of piping system and the experimental results. The comparisons show that the tube is destabilized as the magnitude of the attached mass increases, and stabilized as the position of the attached mass closes to the fixed end. In case of a small end-mass, the system shows complicated and different types of solutions. For a constant end-mass. the system undergoes a series of bifurcations after the first Hopf bifurcation, as the flow velocity increases. which causes chaotic motions of the tube eventually.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2005년도 추계학술대회논문집
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• pp.293-296
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• 2005

This paper is concerned with the sweeping damping controller for beam. The active damping characteristics can be enhanced by moving the damper along the longitudinal axis. In this paper, the equation of motion for a beam including a sweeping damping controller is derived and its stability is proved by using Lyapunov stability theorem. It is found from the theoretical study that the sweeping damping controller can enhance the active damping characteristics, so that a single damper can suppress all the vibration modes of the beam. To demonstrate the concept of the sweeping damping control, the eddy current damper was applied to a cantilever, where the eddy current damping can move along the axis. The experimental result shows that the sweeping eddy current damper Is an effective device for vibration suppression.

• 대한수학회지
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• 제56권3호
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• pp.825-855
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• 2019

We establish the existence of $C^1$ stable invariant manifolds for differential equations $u^{\prime}=A(t)u+f(t,u,{\lambda})$ obtained from sufficiently small $C^1$ perturbations of a nonuniform exponential dichotomy. Since any linear equation with nonzero Lyapunov exponents has a nonuniform exponential dichotomy, this is a very general assumption. We also establish the $C^1$ dependence of the stable manifolds on the parameter ${\lambda}$. We emphasize that our results are optimal, in the sense that the invariant manifolds are as regular as the vector field. We use the fiber contraction principle to establish the smoothness of the invariant manifolds. In addition, we can also consider linear perturbations, and thus our results can be readily applied to the robustness problem of nonuniform exponential dichotomies.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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• pp.953-955
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• 1993

In this paper we propose a new stability theorem and a robust stability condition for linguistic fuzzy model systems in state space. First we define a stability in linear sense. After representing the fuzzy model by a system with disturbances, A necessary and sufficient condition for the stability is derived. This condition is proved to be a sufficient condition of the fuzzy model. The Q in the Lyapunov equation is iteratively adjusted by an gradient-based algorithm to improve its stability test. Finally, stability robustness bounds of a system having modeling error is derived. An example is also included to show that the stability test is powerful.

• 한국항행학회논문지
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• 제20권5호
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• pp.475-481
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• 2016

본 논문에서는 상태변수에 시변 지연시간이 있는 선형 이산 구간 시변 시스템의 안정조건을 새롭게 제안한다. 고려한 시스템은 지연 없는 상태변수에 대한 시스템 행렬과 지연 상태변수에 대한 시스템 행렬이 시변 구간 행렬로 표현되며, 지연시간도 구간에 대하여 시변인 특성을 갖는다. 제안된 안정조건은 리아프노프 안정 이론을 이용하여 유도되며, 매우 간단한 부등식의 형태로 표현된다. 본 논문에서는 기존의 시불변 구간 행렬의 안정성 문제를 시변 구간 행렬의 안정성 문제로 확장하고, 기존에 발표된 결과를 포함하는 강력한 안정조건이 유도된다. 이 안정조건의 유도과정에서는 복잡한 선형행렬부등식 혹은 리아프노프 방정식의 상한 해 한계를 구하지 않아도 된다. 또한, 기존의 결과들과의 비교를 통하여 제안된 안정조건이 많은 기존 안정 조건들을 포함할 수 있음을 보인다. 기존 수치예제를 일반적인 형태로 확장하였고 이에 대하여 새로운 안정조건의 확장성과 효용성을 확인한다.

• 한국항행학회논문지
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• 제23권6호
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• pp.577-583
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• 2019

음이 아닌 입력에 대하여 음이 아닌 초기상태에서 출발한 모든 상태변수 값들이 시간에 대하여 항상 음이 아닌 값을 유지하는 시스템은 양의 시스템으로 정의된다. 본 논문에서는 상태변수에 시변 지연시간과 비구조화된 불확실성이 함께 존재하는 양의 시변 선형 이산 구간 시스템의 안정조건을 새롭게 제안한다. 시변 지연시간은 변동가능한 최소와 최대 지연시간 범위 내에서 변하는 것으로 고려되며, 불확실성은 비선형성을 포함하여 그 최대 크기만을 알 수 있는 것으로 고려한다. 제안된 안정조건은 이전의 결과들이 시불변시스템에만 적용되었거나 불확실성에 대한 고려가 없었던 것을 개선한 것으로 매우 간단한 부등식의 형태로 표현된다. 안정조건은 리아프노프 안정이론을 이용하여 유도되며, 리아프노프 방정식의 상한 해 한계(upper solution bound)를 이용한 기존 결과에 비하여 많은 장점을 갖는다. 제안된 안정조건은 기존의 결과들을 포함하는 효과적인 것으로 수치예제를 통하여 이를 검증한다.