• Korean Journal of Mathematics
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• 제21권3호
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• pp.345-350
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• 2013

Some results on the sensitivity of the solution of the generalized Lyapunov equation $$A^{n-1}X+A^{n-2}XA^*+{\cdots}+X(A^*)^{n-1}=B$$ are shown follow easily from well-known theorems in functional analysis.

• 전자공학회논문지SC
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• 제46권4호
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• pp.49-57
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• 2009

이 논문에서는 특별한 형태의 일반화된 연속시간 Lyapunov 방정식과 해의 존재성에 대해 다룬다. 이것은 무한대의 고유치를 가지는 descriptor 시스템에 대해 시스템의 안정성을 분석하기 위해 필요하다. 주요결과로써 먼저 지수 1과 2를 가지는 경우의 descriptor시스템에 대해 안정성을 위한 필요충분조건을 먼저 제안하고 다음으로 일반적인 경우의 descriptor 시스템에 대하여 특별한 형태의 Lyapunov 방정식을 이용하여 비슷한 안정성 조건을 제안한다. 마지막으로 제안한 방법의 타당성을 보이기 위한 예제를 살펴본다.

• 대한수학회보
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• 제60권1호
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• pp.257-279
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• 2023

Applying the Lyapunov-Schmidt reduction, we consider spectral stability of small amplitude stationary periodic solutions bifurcating from an equilibrium of the generalized Swift-Hohenberg equation. We follow the mathematical framework developed in [15, 16, 19, 23] to construct such periodic solutions and to determine regions in the parameter space for which they are stable by investigating the movement of the spectrum near zero as parameters vary.

• International Journal of Control, Automation, and Systems
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• 제1권4호
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• pp.459-463
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• 2003

In this paper, new results using bounds for the solution of the discrete Lyapunov matrix equation are proposed, and some of the existing works are generalized. The bounds obtained are advantageous in that they provide nontrivial upper bounds even when some existing results yield trivial ones.

• 제어로봇시스템학회논문지
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• 제18권6호
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• pp.513-518
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• 2012

In this paper, we propose a generalized index independent stability condition for a descriptor systemwithout any transformations of system matrices. First, the generalized Lyapunov equation with a specific right-handed matrix form is considered. Furthermore, the existence theorem and the necessary and sufficient conditions for asymptotically stable descriptor systems are presented. Finally, some suitable examples are used to show the validity of the proposed method.

• International Journal of Control, Automation, and Systems
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• 제2권4호
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• pp.516-522
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• 2004

In this paper we investigate the properties of a generalized impulse response Gramian. The recursive relationship satisfied by the family of Gramians is established. It is shown that the generalized impulse response Gramian contains information on the characteristic polynomial of a linear time-invariant continuous system. The results are applied to model reduction problem.

• 전자공학회논문지SC
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• 제46권1호
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• pp.34-42
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• 2009

이 논문에서는 델타연산자를 사용하는 단일접근법에 의해 분산 특이변동 시스템에 대한 리아프노프 행렬 방정식에 대한 경계치의 새로운 결과가 제시되었고 기존의 연구결과들 중 결함이 있는 가정에 의해 얻어진 것들에 대한 보편화 작업도 수행되었다.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 1997년도 추계학술대회논문집; 한국과학기술회관; 6 Nov. 1997
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• pp.145-153
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• 1997

Dynamic characteristics are investigated when a nonlinear system showing periodic and chaotic responses under harmonic excitation is exposed to random perturbation. About two well potential problem, probability of homoclinic bifurcation is estimated using stochastic generalized Meinikov process and quantitive characteristics are investigated by calculation of Lyapunov exponent. Critical excitaion is calculated by various assumptions about Gaussian Melnikov process. To verify the phenomenon graphically Fokker-Planck equation is solved numerically and the original nonlinear equation is numerically simulated. Numerical solution of Fokker-Planck equation is calculated on Poincare section and noise induced chaos is studied by solving the eigenvalue problem of discretized probability density function.

• 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.