• 산업기술연구
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• 제14권
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• pp.19-28
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• 1994

일반적으로 2차원 Poisson 방정식을 풀기 위해 유한 차분법을 이용하여 tridiagonal block Toeplitz 선형방정식을 얻는다. 이 선형방정식의 독특한 형태를 활용하기 위해 Lyapunov 방정식으로 변화시킨 다음 이산정현변환(DST)을 이용해서 대각선 행렬로 만들면 계산이 용이해진다. 또 DST는 FFT를 이용해 계산할 수 있으므로 고속 계산이 가능하다. FFT를 병렬로 처리하기 위해 프로세서가 4,096개인 SIMD 컴퓨터 MP-2에서 시뮬레이션했다. 본 논문에서는 알고리즘 유도, 매핑 및 시뮬레이션 결과를 제시했다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2005년도 학술대회 논문집 정보 및 제어부문
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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.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1999년도 제14차 학술회의논문집
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• pp.112-115
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• 1999

A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N-th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed. The proposed stability condition ensures stability of a discrete state delay system whose state delay is not exactly known but only known to lie in a certain interval.

• 전기학회논문지
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• 제56권11호
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• pp.2023-2026
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• 2007

In this letter, the problem for a class of neutral differential equation is considered. Based on the Lyapunov method, a stability criterion, which is delay-dependent on both ${\tau}\;and\;{\sigma}$, is derived in terms of linear matrix inequality (LMI). Two numerical examples are carried out to support the effectiveness of the proposed method.

• 대한전기학회논문지:전력기술부문A
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• 제48권5호
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• pp.560-570
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• 1999

This paper formulates the suboptimal robust Kalman filtering problem into two coupled Linear Matrix Inequality (LMI) problems by applying Lyapunov theory to the augmented system which is composed of the state equation in the uncertain linear system and the estimation error dynamics. This formulations not only provide the sufficient conditions for the existence of the desired filter, but also construct the suboptimal robust Kalman filter. The proposed filter can guarantee the optimized upper bound of the estimation error variance for uncertain systems with parametric uncertainties in both the state and measurement matrices. In addition, this paper shows how the problem of finding the minimizing solution subject to Quadratic Matrix Inequality (QMI), which cannot be easily transformed into LMI using the usual Schur complement formula, can be successfully modified into a generic LMI problem.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1996년도 한국자동제어학술회의논문집(국내학술편); 포항공과대학교, 포항; 24-26 Oct. 1996
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• pp.28-31
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• 1996

We propose an estimator design method of Stewart platform, which gives the 6DOF, positions and velcities of Stewart platform from the measured cylinder length. The solution of forward kinematics is not solved yet as a useful realtime application tool because of the complexity of the equation with multiple solutions. Hence we suggest an nonlinear estimator for the forward kinematics solution using Luenberger observer with nonlinear error correction term. But the way of residual gain selection of the estimator is not clear, so we suggest an algebraic Riccati equation for gain matrix using Lyapunov method. This algorithm gives the sufficient condition of the stability of error dynamics and can be extended to general nonlinear system.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1988년도 한국자동제어학술회의논문집(국제학술편); 한국전력공사연수원, 서울; 21-22 Oct. 1988
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• pp.1051-1054
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• 1988

In this paper we present initial convergence properties of the Kalman filtering algorithm, we put an arbitrary small positive correlation matrix as an initial condition in the recursive algorithm. This arbitrary small initial condition perturbs the Kalman filtering algorithm and may lead to initial instability. We derive a condition which insures the stable operation of the Kalman filtering algorithm from the stochastic Lyapunov difference equation.

• 제어로봇시스템학회논문지
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• 제5권7호
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• pp.794-799
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• 1999

This study deals with robustness bounds estimation for uncertain linear systems with structured perturbations where the eigenvalues of the perturbed systems are guaranteed to stay in a prescribed region. Based upon the Lyapunov approach, new theorems to estimate allowable perturbation parameter bounds are derived. The theorems are referred to as the zero-order or first-order asymmetric robustness measure depending on the order of the P matrix in the sense of Taylor series expansion of perturbed Lyapunov equation. It is proven that Gao's theorem for the estimation of stability robustness bounds is a special case of proposed zero-order asymmetric robustness measure for eigenvalue assignment. Robustness bounds of perturbed parameters measured by the proposed techniques are asymmetric around the origin and less conservative than those of conventional methods. Numerical examples are given to illustrate proposed methods.

• 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.

• 대한수학회논문집
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• 제31권3호
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• pp.603-611
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• 2016

In this paper, we show that if $\mathcal{A}$ is a differential subalgebra of Banach algebras $\mathcal{B}({\ell}^r)$, $1{\leq}r{\leq}{\infty}$, then solutions of the infinite dimensional linear system associated with a matrix in $\mathcal{A}$ have its p-exponential stability being equivalent to each other for different $1{\leq}p{\leq}{\infty}$.