• Bulletin of the Korean Mathematical Society
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• v.51 no.1
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• pp.237-252
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• 2014

In this paper, we give a necessary and sufficient condition for the hyponormality of the block Toeplitz operators $T_{\Phi}$, where ${\Phi}$ = $F+G^*$, F(z), G(z) are some matrix valued polynomials on the vector valued Bergman space $L^2_a(\mathbb{D},\mathbb{C}^n)$. We also show some necessary conditions for the hyponormality of $T_{F+G^*}$ with $F+G^*{\in}h^{\infty}{\otimes}M_{n{\times}n}$ on $L^2_a(\mathbb{D},\mathbb{C}^n)$.

• Proceedings of the KIEE Conference
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• 2006.11a
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• pp.342-344
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• 2006

The modem enormous electric power system has made power system analysis much more complex and difficult. For effective analysis of the power system, model reduction and aggregation is required. In this paper, a new aggregation method is presented to aggregate the coherent generators in the large scale power system while matching the power flow. In order to demonstrate the effects of this aggregation method, it is applied to a small scale power system. A multi-variable control technique of $H_{\infty}$ control is also applied to enhance the dynamic stability of the aggregated power system.

• Korean Journal of Mathematics
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• v.26 no.1
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• pp.103-127
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• 2018

This paper is dedicated to studying some Hausdorff operators on the Heisenberg group ${\mathbb{H}}^n$. The sharp bounds on the strong-type weighted Lorentz spaces ${\Lambda}^p_u(w)$ and the weak-type weighted Lorentz spaces ${\Lambda}^{p,{\infty}}_u(w)$ are investigated. Especially, the results cover the classical power weighted space $L^{p,q}_{\alpha}$. The results are also extended to the product spaces ${\Lambda}^{p_1}_{u_1}(w_1){\times}{\Lambda}^{p_2}_{u_2}(w_2)$, especially for $L^{p_1,q_1}_{{\alpha}_1}{\times}L^{p_2,q_2}_{{\alpha}_2}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.855-868
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• 1998

For a random sample of size n from general linear model, $Y_i= heta(X_i)+varepsilon_i,;let Y_{in}$ denote the ith oder statistics of the Y sample values. The X-value associated with $Y_{in}$ is denoted by $X_{[in]}$ and is called the concomitant of ith order statistics. The estimator of the location of a maximum of a regression function, $ heta$($\chi$), was proposed by (equation omitted) and was found the convergence rate of it under certain weak assumptions on $ heta$. We will discuss the asymptotic distributions of both $ heta(X_{〔n-r+1〕}$) and (equation omitted) when r is fixed as nolongrightarrow$\infty$(i.e. extreme case) on the basis of the theorem of the concomitants of order statistics. And the will investigate the asymptotic behavior of Max｛$\theta$( $X_{〔n-r+1:n〕/}$ ), . , $\theta$( $X_{〔n:n〕}$)｝as an estimator for the peak of a regression function.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.523-533
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• 2007

Let $\cal{B}$ be a reflexive Banach space of functions analytic on the open unit disc and M be an invariant subspace of the multiplication operator by the independent variable, $M_z$. Suppose that $\varphi\;\in\;\cal{H}^{\infty}$ and $M_{\varphi}$ : M ${\rightarrow}$ M, defined by $M_{\varphi}f={\varphi}f$, is the operator of multiplication by ${\varphi}$. We would like to investigate the spectrum and the essential spectrum of $M_{\varphi}$ and we are looking for the necessary and sufficient conditions for $M_{\varphi}$ to be a Fredholm operator. Also we give a sufficient condition for a sequence $\{w_n\}$ to be an interpolating sequence for $\cal{B}$. At last the commutant of $M_{\varphi}$ under certain conditions on M and ${\varphi}$ is determined.

• 제어로봇시스템학회:학술대회논문집
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• 1994.10a
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• pp.16-19
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• 1994

This paper describes a design method of compensators for decentralized control systems. Decentralized control problem is convenient to design multi-variable control systems and formulated as a series of independent designs. The proposed design method is composed of some steps, which is sequentially to close loop of the system diagonalized by regarding interactive subsystem as perturbation for current loop. So, on the basis of H$_{\infty}$ control theory, decentralized controllers are designed considering robust stability for diagonal systems with perturbations. A numerical example shows that the proposed design method is effective for multivariable control systems..

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.779-782
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• 1996

Repetitive control is a proposed control strategy in view of the internal model principle and achieves a high accuracy asymptotic tracking property by implementing a model that generates the periodic signals of period into the closed-loop system. Since the repetitive control system contains a periodic signal generator with positive feedback loop, which reduces the stability margin, in the overall closed-loop system, the stability of the closed-loop system should be considered as an important problem. In case that a real system has plant uncertainties which are not represented through modeling, the robust stability problem of the repetitive control system has not been considered sufficiently. In this paper, we propose the robust stability condition for the system with modeling uncertainty. The proposed robust stability condition will be obtained using the robust performance condition in the H$_{\infty}$ control. Moreover, by use of the proposed robust stability condition, we propose a procedure that designs a repetitive controller and a feedback controller simultaneously which can stabilize the overall closed-loop system robustly and which can also do the closedloop system without repetitive controller..

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.976-979
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• 1996

Teleoperation is the extension of a person's sensing and manipulation capability to a remote location. Teleoperators generally can be modeled as linear transfer function indecently including modeling uncertainty. Modeling uncertainties can make the system unstable and its performance poor. Thus I'm studying about a design framework for a bilateral controller of teleoperator systems with modeling uncertainties. In this paper, a method based on the H$_{\infty}$-optimal control and .mu.-synthesis frameworks are introduced to design a controller for the teleoperator that achieves stability and performance in the presence of the modeling uncertainties..ties.inties.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.1092-1097
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• 2005

In this paper, design approach of PID controller with rejection function against external disturbance in motor control system is proposed using bacterial foraging based optimal algorithm. Up to the present time, PID Controller has been used to operate for AC motor drive because of its implementational advantages in practice and simple structure. However, it is not easy to achieve an optimal PID gain with no experience, since the gain of the PID controller has to be manually tuned by trial and error in the industrial system with disturbance. To design disturbance rejection tuning, disturbance rejection conditions based on $H_{\infty}$ are illustrated and the performance of response based on the bacterial foraging is computed for the designed PID controller as ITSE (Integral of time weighted squared error). Hence, parameters of PID controller are selected by bacterial foraging based optimal algorithm to obtain the required response

• Journal of Institute of Control, Robotics and Systems
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• v.15 no.10
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• pp.988-993
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• 2009

In this paper, we deal with a tracking gain-up controller design problem to control effectively the shake of tracking actuator after a track seek. A minimum tracking gain-up open-loop gain can be calculated by estimating the shake of tracking actuator and a desired transient specification is considered to diminish effectively the shake of actuator. A tracking gain-up controller is designed by considering a robust $H_{\infty}$ control problem with a regional stability constraint. The proposed tracking gain-up controller design method is applied to the track-following system of a DVD recording device and is evaluated through the experimental results.