• Proceedings of the KIEE Conference
• /
• 1991.07a
• /
• pp.678-681
• /
• 1991

In this paper, we propose a robust linear time-invariant feedback compensator design methodology for multivariable system which have both matched and mismatched uncertainties. In order to attack the problem of designing robust compensators guaranteeing uniform ultimate boundedness of every closed-loop system response within an arbitrarily small ball centered at the zero state based solely on the knowledge of the upper norm-bounds of uncertainties, we use an approach based upon the comparison theorem which is an effective approach in studying augmented feedback control systems with both mismatched and matched uncertainties. Through the approach, we draw some sufficient conditions for robust stability, and we give a simple example.

• Journal of the Korean Mathematical Society
• /
• v.40 no.6
• /
• pp.999-1014
• /
• 2003

For a fixed function h we deal with a class of convolution transforms $f\;{\rightarrow}\;f\;*\;h$, where $(f\;*\;h)(x)\;=\frac{1}{2x}\;{\int_{{R_{+}}^2}}^{e^1{\frac{1}{2}}(x\frac{u^2+y^2}{uy}+\frac{yu}{x})}\;f(u)h(y)dudy,\;x\;\in\;R_{+}$ as integral operators $L_p(R_{+};xdx)\;\rightarrow\;L_r(R_{+};xdx),\;p,\;r\;{\geq}\;1$. The Young type inequality is proved. Boundedness properties are investigated. Certain examples of these operators are considered and inversion formulas in $L_2(R_{+};xdx)$ are obtained.

• Journal of the Korean Mathematical Society
• /
• v.55 no.4
• /
• pp.939-962
• /
• 2018

In this paper, we show that the commutator of the intrinsic square function with BMO symbols is bounded on the variable exponent Lebesgue spaces $L^{p({\cdot})}({\mathbb{R}}^n)$ applying a generalization of the classical Rubio de Francia extrapolation. As a consequence we further establish its boundedness on the variable exponent Morrey spaces $\mathcal{M_{p({\cdot}),u}$, Morrey-Herz spaces $M{\dot{K}}^{{\alpha}({\cdot}),{\lambda}}_{q,p({\cdot})}({\mathbb{R}}^n)$ and Herz type Hardy spaces $H{\dot{K}}^{{\alpha}({\cdot}),q}_{p({\cdot})}({\mathbb{R}}^n)$, where the exponents ${\alpha}({\cdot})$ and $p({\cdot})$ are variable. Observe that, even when ${\alpha}({\cdot}){\equiv}{\alpha}$ is constant, the corresponding main results are completely new.

• Communications of the Korean Mathematical Society
• /
• v.32 no.3
• /
• pp.567-578
• /
• 2017

Many scholars studied the boundedness of $Ces{\grave{a}}ro$ operators between $Q_K$ spaces and Bloch spaces of holomorphic functions in the unit disc in the complex plane, however, they did not describe the compactness. Let 0 < ${\alpha}$ < $+{\infty}$, K(r) be right continuous nondecreasing functions on (0, $+{\infty}$) and satisfy $${\displaystyle\smashmargin{2}{\int\nolimits_0}^{\frac{1}{e}}}K({\log}{\frac{1}{r}})rdr<+{\infty}$$. Suppose g is a holomorphic function in the unit disk. In this paper, some sufficient and necessary conditions for the extended $Ces{\grave{a}}ro$ operators $T_g$ between ${\alpha}$-Bloch spaces and $Q_K$ spaces in the unit disc to be bounded and compact are obtained.

• Proceedings of the KIEE Conference
• /
• 1992.07a
• /
• pp.347-350
• /
• 1992

In this note, we propose a method for designing a robot controller which can suppress the effects of both the model uncertainty and noisy velocity measurements. The controller is an output feedback compensator of which the constant gains are given in terms of a Riccati equation and a Lyapunov equation. The controller guarantees not only uniform boundedness but uniform ultimate boundedness. The stability result is local but the region can be arbitrarily enlarged at the expense of large control gain. The control law needs neither the exact knowledge of the physical robot parameters nor clean velocity measurements.

• Language and Information
• /
• v.14 no.1
• /
• pp.93-111
• /
• 2010

This article is a description of the case variation in Guarani Language, which is a relatively, rarely studied language, and more so about case phenomena. Guarani has two remarkable facts about case. First, it has two overt accusative case markers, which are differentiated by the semantic notion of boundedness as in Jackendoff(1990, 1991). The existence of accusative case markers in Guarani is attested by their behavior in the typical transitive verb sentences, the ability to occur in ECM constructions, and the interpretation of specificity which is parallel to Turkish accusative case marker realization reported in Enc(1991). Second, accusative case forms occur in adjunct positions as well as object positions in Guarani. To capture these peculiar case phenomena, an account based on some recent Minimalist ideas about case checking from Legate(2008), Bowers(2010) is shown to be available.

• Journal of the Korean Society for Precision Engineering
• /
• v.30 no.12
• /
• pp.1287-1293
• /
• 2013

In this paper, we consider variable speed wind turbine systems containing uncertain elements. Though PI controller is generally used for pitch control, it cannot guarantee a stability and performance of the complicated wind turbine systems. A robust pitch control scheme is proposed to regulate the electric power output above the rated wind speed. The pitch controller is designed in order to guarantee uniform boundedness and uniform ultimate boundedness based on the bound values of the set where the uncertainties are laid or moves. In order to verify the proposed control scheme, we present stability analysis and simulation results using Matlab/Simulink.

• Journal of applied mathematics & informatics
• /
• v.22 no.1_2
• /
• pp.247-262
• /
• 2006

The main objective of this paper is to study the boundedness character, the periodic character and the global stability of the positive solutions of the following difference equation $x_{n+1}=\frac{{\alpha}x_n+{\beta}x_{n-1}+{\gamma}x_{n-2}+{\delta}x_{n-3}}{Ax_n+Bx_{n-1}+Cx_{n-2}+Dx{n-3}}$, n=0, 1, 1, ... where the coefficients A, B, C, D, ${\alpha},\;{\beta},\;{\gamma},\;{\delta}$ and the initial conditions x-3, x-2, x-1, x0 are arbitrary positive real numbers.

• Journal of applied mathematics & informatics
• /
• v.29 no.3_4
• /
• pp.1017-1025
• /
• 2011

In this paper, we survey various notions and results related to statistical convergence of a sequence of fuzzy numbers, in which statistical convergence for fuzzy numbers was first introduced by Nuray and Savas in 1995. We will go over boundedness, convergence of sequences of fuzzy numbers, statistically convergence and statistically Cauchy sequences of fuzzy numbers, statistical limit and cluster point for sequences of fuzzy numbers, statistical mono-tonicity and boundedness of a sequence of fuzzy numbers and finally statistical limit inferior and limit inferior for the statistically bounded sequences of fuzzy numbers.

• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.217-230
• /
• 2017

In this paper we deal with the difference equation $$y_{n+1}=\frac{ay_{n-1}}{by_ny_{n-1}+cy_{n-1}y_{n-2}+d}$$, $$n{\in}\mathbb{N}_0$$, where the coefficients a, b, c, d are positive real numbers and the initial conditions $y_{-2}$, $y_{-1}$, $y_0$ are nonnegative real numbers. Here, we investigate global asymptotic stability, periodicity, boundedness and oscillation of positive solutions of the above equation.