• Journal of Institute of Control, Robotics and Systems
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• v.14 no.3
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• pp.226-231
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• 2008

In this paper, we propose novel eigenstructure assignment method in full-state feedback for linear time-invariant MIMO system such that directions of some left eigenvectors are exactly assigned to the desired directions. It is required to consider the direction of left eigenvector in designing eigenstructure of closed-loop system, because the direction of left eigenvector has influence over excitation by associated input variables in time-domain response. Exact direction of a left eigenvector can be achieved by assigning proper right eigenvector set satisfying the conditions of the presented theorem based on Moore's theorem and the orthogonality of left and right eigenvector. The right eigenvector should reside in the subspace given by the desired eigenvalue, which restrict a number of designable left eigenvector. For the two cases in which desired eigenvalues are all real and contain complex number, design freedom of designable left eigenvector are given.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.10
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• pp.895-901
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• 2012

The stability robustness problem of linear discrete systems with time-varying unstructured uncertainty of delayed states with time-varying delay time is considered. The proposed conditions for stability can be used for finding allowable bounds of timevarying uncertainty and delay time, which are solved by using LMI (Linear Matrix Inequality) and GEVP (Generalized Eigenvalue Problem) known as powerful computational methods. Furthermore, the conditions can imply the several previous results on the uncertainty bounds of time-invariant delayed states. Numerical examples are given to show the effectiveness of the proposed algorithms.

• Kyungpook Mathematical Journal
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• v.58 no.3
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• pp.489-494
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• 2018

The first purpose of this note is to generalize two nice theorems of H. J. Kim concerning hyperinvariant subspaces for certain classes of operators on Hilbert space, proved by him by using the technique of "extremal vectors". Our generalization (Theorem 1.2) is obtained as a consequence of a new theorem of the present authors, and doesn't utilize the technique of extremal vectors. The second purpose is to use this theorem to obtain the existence of hyperinvariant subspaces for a class of $2{\times}2$ operator matrices (Theorem 3.2).

• Smart Structures and Systems
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• v.25 no.1
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• pp.37-45
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• 2020

This paper aims at enlightening the properties, computational and implementation issues related to Kalman filter based state estimation algorithms and sliding mode observers, by applying them for estimating the states of a smart structure system. The Kalman based estimators considered in this work are Kalman filter and information filter and, the sliding mode observers considered are Utkin observer and higher order sliding mode observer. A fourth order linear time invariant model of a piezo actuated beam is used in this work. This structure is embedded with four number of piezo patches, of which two act as sensors, one as disturbance actuator and the other as control actuator. The performance of the state estimation algorithms is evaluated through simulation, for the first two vibrating modes of the piezo actuated structure, when the structure is maintained at first mode and second mode resonance.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.5 no.3
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• pp.179-186
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• 1993

The characteristics of pressure-drop oscillations(PDO) in boiling channel are studied experimentally. The effects of initial and boundary conditions on PDO are investigated in terms of oscillation period and amplitude. The period and amplitude of PDO are increased with the increase in the compressible volume in surge tank and heat input. However the amplitude of PDO is decreased with fluid temperature under low subcooling condition. Higher initial insurge flowrate resulted in almost invariant oscillation period but lower amplitude. At higher heat input the oscillation of heater wall temperature is significant, whose period is the same as that of pressure-drop instability.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.6
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• pp.517-523
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• 2006

This paper is focused on a robust saturation controller for the stable linear time-invariant (LTI) system involving both actuator's saturation and structured real parameter uncertainties. Based on affine quadratic stability and multi-convexity concept, a robust saturation controller is newly proposed and the linear matrix inequality (LMI)-based sufficient existence conditions for this controller are presented. The controller suggested in this paper can analytically prescribe the lower and upper bounds of parameter uncertainties, and guarantee the closed-loop robust stability of the system in the presence of actuator's saturation. Through numerical simulations, it is confirmed that the proposed robust saturation controller is robustly stable with respect to parameter uncertainties over the prescribed range defined by the lower and upper bounds.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.207-212
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• 2001

In this paper, a method to be able to decide the possible maximum gain of P, PI control for the retarded processes under stable condition is proposed. At first, adjustable parameter set causing stability limit are obtained based on the frequency domain condition which makes the roots of transfer function locate on the $j\omega$ axis. And the cut-in frequency $\omega{_p}$ to bring the parameter set to P control from PI control is derived by an equation with 2 parameters L and $T_m$ given, then $\omega{_p}$ is used to compute the maximum gain with stable condition. For the calculation, the controlled process of first order system with time delay element is introduced and all parameters are presumed to be time invariant.

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• Kyungpook Mathematical Journal
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• v.59 no.2
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• pp.225-231
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• 2019

In a previous paper, the authors of this paper studied $2{\times}2$ matrices in upper triangular form, whose entries are operators on Hilbert spaces, and in which the the (1, 1) entry has a nontrivial hyperinvariant subspace. We were able to show, in certain cases, that the $2{\times}2$ matrix itself has a nontrivial hyperinvariant subspace. This generalized two earlier nice theorems of H. J. Kim from 2011 and 2012, and made some progress toward a solution of a problem that has been open for 45 years. In this paper we continue our investigation of such $2{\times}2$ operator matrices, and we improve our earlier results, perhaps bringing us closer to the resolution of the long-standing open problem, as mentioned above.

• Journal of the Korean Mathematical Society
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• v.59 no.2
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• pp.337-352
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• 2022

We consider the set of points with historic behavior (which is also called the irregular set) for continuous flows and suspension flows. In this paper under the hypothesis that (X_t)_t is a continuous flow on a d-dimensional Riemaniann closed manifold M (d ≥ 2) with gluing orbit property, we prove that the set of points with historic behavior in a compact and invariant subset ∆ of M is either empty or is a Baire residual subset on ∆. We also prove that the set of points with historic behavior of a suspension flows over a homeomorphism satisfyng the gluing orbit property is either empty or Baire residual and carries full topological entropy.