• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1995년도 Proceedings of the Korea Automation Control Conference, 10th (KACC); Seoul, Korea; 23-25 Oct. 1995
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• pp.332-335
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• 1995

A simple and effective method for improving Euclidean norm condition number for chemical processing system is presented. The singular value sensitivities of Freudenberg et al. (1982) is used to estimate the behavior of singular values of process transfer function matrix when design parameter is changed, then the condition number can be calculated straightforwardly. The method requires explicit dependencies of each transfer function matrix elements on design parameters. These dependencies can be obtained either by symbolic differentiation in the form of explicit function of design parameters, or by numerical perturbation studies for units with large and complicated models. Gerschgorin-type lower bound for minimum singular value is introduced to detect the large divergencies near singular point due to linearity of sensitivities. The case studies are performed to show the efficiency of the proposed method.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.326-326
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• 2000

Continuous time system deadbeat controller(CdbC) has been studied mainly since 1992 especially by Japan researchers. They suggested delay elements. These elements stem from the finite Laplace Transform which is the starting point in deadbeat control system design in continuous time system. Every transfer function is established by these elements. From some conditions such as internal model stability and peasibility of a CdbC controller. unknown polynomials or coefficients can be calculated. In this paper, optimal pole placement of the closed loop system is suggested. From this. a CdbC controller with lower order can be obtained which attains the same level of weighted sensitivity function's H$_{\infty}$ norm used as a measure of the robustness property as existing CdbCs.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권4호
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• pp.409-416
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• 2015

In many practical applications, we face the problem of reconstruction of an unknown function sampled at some data points. Among infinitely many possible reconstructions, the thin plate spline interpolation is known to be the least oscillatory one in the Beppo-Levi semi norm, when the data points are sampled in $\mathbb{R}^2$. The traditional proofs supporting the argument are quite lengthy and complicated, keeping students and researchers off its understanding. In this article, we introduce a simple and short proof for the optimal reconstruction. Our proof is unique and reguires only elementary mathematical background.

• Korean Journal of Mathematics
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• 제29권2호
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• pp.361-370
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• 2021

Let 𝕂 be a complete ultrametric algebraically closed field and 𝓐 (𝕂) be the 𝕂-algebra of entire function on 𝕂. For any p-adic entire functions f ∈ 𝓐 (𝕂) and r > 0, we denote by |f|(r) the number sup {|f (x)| : |x| = r} where |·|(r) is a multiplicative norm on 𝓐 (𝕂). In this paper we study some growth properties of composite p-adic entire functions on the basis of their relative (p, q)-𝜑 order where p, q are any two positive integers and 𝜑 (r) : [0, +∞) → (0, +∞) is a non-decreasing unbounded function of r.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제9권2호
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• pp.99-106
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• 2005

We present a relation between the orthogonality of the constrained Legendre polynomials over the triangular domain and the BB ($B{\acute{e}zier}\;-Bernstein$) coefficients of the polynomials using the equivalence of orthogonal complements. Using it we also show that the best constrained degree reduction of polynomials in BB form equals the best approximation of weighted Euclidean norm of coefficients of given polynomial in BB form from the coefficients of polynomials of lower degree in BB form.

• 대한수학회논문집
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• 제20권3호
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• pp.505-509
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• 2005

We show that every $\varepsilon-approximate$ Jordan functional on a Banach algebra A is continuous. From this result we obtain that every $\varepsilon-approximate$ Jordan mapping from A into a continuous function space C(S) is continuous and it's norm less than or equal $1+\varepsilon$ where S is a compact Hausdorff space. This is a generalization of Jarosz's result [3, Proposition 5.5].

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.487-498
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• 2010

For some $\phi$-sequences $\phi_1$, $\phi_2$ and $\phi_3$, and $\kappa$-function $\kappa_1$, $\kappa_2$ and $\kappa_3$ with $\kappa_1^{-1}(x)\kappa_2^{-1}(x)\;{\geq}\;\kappa_3^{-1}(x)$ for $x\;{\geq}\;0$, the Luxemburg norm is lower semi-continuous on ${\kappa}{\phi}BV_0$, and some specialized equivalent conditions are considered.

• 대한수학회보
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• 제33권3호
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

• 대한수학회보
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• 제51권3호
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• pp.803-812
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• 2014

Let ${\mathcal{S}}^0_{\mathcal{H}}$ be the class of normalized univalent harmonic mappings in the unit disk. A subclass ${\mathcal{V}}^{\mathcal{H}}(k)$ of ${\mathcal{S}}^0_{\mathcal{H}}$, whose analytic part is function with bounded boundary rotation, is introduced. Some bounds for functionals, specially harmonic pre-Schwarzian derivative, described in ${\mathcal{V}}^{\mathcal{H}}(k)$ are given.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.471-476
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• 1993

In this paper we proposed the digital implementation of an $H^{\infty}$-optimal controller using lifting technique and $H^{\infty}$-control theory. The discrete controller is obtained through iterative adjustment of sampling time and weighting function, which can ber performed by computing the L$_{2}$-induced input to output norm of the sampled-data system with bandlimited exogenous input. The resulting sampled-data bandlimited exogenous input. The resulting sampled-data system is stable and the performance including inter-sampling behaviour of the hybrid system can be also optimized.d.