• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.9
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• pp.431-438
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• 2001

This paper present experimental results of source identification for non-minimum phase system. Generally, a causal linear system may be described by matrix form. The inverse problem is considered as a matrix inversion. Direct inverse method can\`t be applied for a non-minimum phase system, the reason is that the system has ill-conditioning. Therefore, in this study to execute an effective inversion, SVD inverse technique is introduced. In a Non-minimum phase system, its system matrix may be singular or near-singular and has one more very small singular values. These very small singular values have information about a phase of the system and ill-conditioning. Using this property we could solve the ill-conditioned problem of the system and then verified it for the practical system(cantilever beam). The experimental results show that SVD inverse technique works well for non-minimum phase system.

• The Journal of the Acoustical Society of Korea
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• v.20 no.8
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• pp.3-11
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• 2001

This paper describes an implementation of inverse filter using SVD in order to recover the input in multi-channel system. The matrix formulation in SISO system is extended to MIMO system. In time and frequency domain we investigates the inversion of minimum phase system and non-minimum phase system. To execute an effective inversion of non-minimum phase system, SVD is introduced. First of all we computes singular values of system matrix and then investigates the phase property of system. In case of overall system is non-minimum phase, system matrix has one (or more) very small singular value (s). The very small singular value (s) carries information about phase properties of system. Using this property, approximate inverse filter of overall system is founded. The numerical simulation shows potentials in use of the inverse filter.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.107-116
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• 2012

We investigate the multiple solutions for a class of the elliptic system with the singular potential nonlinearity. We obtain a theorem which shows the existence of the solution for a class of the elliptic system with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and critical point theory.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.483-493
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• 2013

We investigate the multiplicity of the solutions for a class of the system of the biharmonic equations with some singular potential nonlinearity. We obtain a theorem which shows the existence of the nontrivial weak solution for a class of the system of the biharmonic equations with singular potential nonlinearity and Dirichlet boundary condition. We obtain this result by using variational method and the generalized mountain pass theorem.

• Journal of the Korean Institute of Telematics and Electronics
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• v.25 no.12
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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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.2
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• pp.67-80
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• 1998

In this paper the linear algebraic system obtained from a singular integral equation with variable coeffcients by a quadrature-collocation method is considered. We study this underdetermined system by means of the Moore Penrose generalized inverse. Convergence in compact subsets of [-1, 1] can be shown under some assumptions on the coeffcients of the equation.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.11 no.4
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• pp.89-99
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• 2007

In this paper, we define the upper and lower solutions for a p-Laplacian system with singular nonlinearity at the boundaries. And we prove the theorem for the upper and power solutions method.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.449-451
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• 2003

In this paper, the stability problem for singular bilinear system is investigated. We present state feedback control laws for two classes of singular bilinear plants. Asymptotic stability of the closed-loop systems is derived by employing singular Lyapunov's direct method. The primary advantage of our approach lies in its simplicity. In order to verify effectiveness of the results, two numerical examples are given.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1452-1455
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• 1997

This paper studies the problem of approximating commensurate input delay sustems by finite dimensional systems based on the Hankel singular values. I is shown that the Gankel singular values are solutions a trancendental equation and the Hankel singular vectors are obtained form the kernel of the matrix. The computaioin is carried out in state spae framework. Once singular values and vectors are calcualted, finite dimensional approximated systems are constructed using stadnard linear system computational tools. An example is included.

• Journal of Institute of Control, Robotics and Systems
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• v.6 no.1
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• pp.1-7
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• 2000

This paper studies the delay-characteristics using the singular values and vectors of Hankel operators for input delay systems. First, the computational method of Hankel singular values and their corresponding singular vectors are introduced, and then it is analytically provea that all the Hankel singular vlues have a monotone increasing properties as the length of delay time increases. Furthermore, through a simple numerical example, it is shown that the Hankel singular values are dependent only on the ratio of the time constant of a lumped parameter system to the length of delay , and in case that the time constant is relatively larger than the delay time, the lumped parameter characteristic has a great influence on the input delay systems.