• Proceedings of the KIEE Conference
• /
• 2003.11b
• /
• pp.135-138
• /
• 2003

In this paper, we provide a reliable few controller design method for descriptor systems satisfying asymptotic stability with $H_\infty$ norm bound and all actuator failures occurred within the pre-specified subset. The proper condition for the existence of a reliable $H_\infty$ controller and the controller design method are proposed by linear matrix inequality(LMI), Schur complements, and singular value decomposition. All solutions can be obtained simultaneously because the presented sufficient condition can be expressed as an LMI form.

• Journal of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.761-773
• /
• 1995

The nonlinear boundary value problem $$ y" = f(x, y, y') = -\frac{x}{3}y' - \frac{y^2}{g(x)}, 0 < x < 1, $$ $$ (1.1) y'(0) = 0, and either (H) : y(1) = \lambda > 0 $$ $$ or (S) : y'(1) + (1 - \upsilon)y(1) = 0, 1 - \upsilon > 0, $$ $$g \in C[0, 1], k \leq g(x) \leq K on [0, 1] for some k, K > 0 $$ arises in the nonlinear circular membrane under normal pressure [2, 3]., 3].

• Korean Journal of Mathematics
• /
• v.26 no.1
• /
• pp.9-21
• /
• 2018

We investigate existence and multiplicity of the solutions for elliptic boundary value problem with two singularities. We obtain one theorem which shows that there exists at least one nontrivial weak solution under some conditions on which the corresponding functional of the problem satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.

• Journal of applied mathematics & informatics
• /
• v.12 no.1_2
• /
• pp.165-182
• /
• 2003

Toeplitz matrix method and the product Nystrom method are described for mixed Fredholm-Volterra singular integral equation of the second kind with Carleman Kernel and logarithmic kernel. The results are compared with the exact solution of the integral equation. The error of each method is calculated.

• Journal of the Korean Institute of Telematics and Electronics D
• /
• v.34D no.6
• /
• pp.1-10
• /
• 1997

By using the boundary element method, the cahracterization and the circuit modelling of the coplanar waveguide (CPW) discontinuities are performed bvia quasi-static approximation. The capacitive equivalent circuits are obtained by developing the 3-D boundary element method with collocation method. On the triangular patch, the numerical scheme employed the linear basis functions and the analytic solutions of the integrals on the singular points. The capacitive discontinuities of gaps, end-gaps, and open-ends are characterized and the results compared with the conductor backed coplanar waveguides.

• Proceedings of the IEEK Conference
• /
• 2002.07c
• /
• pp.1807-1810
• /
• 2002

This paper presents a technique for avoid- ing indefiniteness in Maximum Likelihood (ML) criteria for Direction-of-Arrival (DOA) finding using a sensor ar- ray with arbitrary configuration. The ML criterion has singular points in the solution space where the criterion becomes indefinite. Solutions fly iterative techniques for ML bearing estimation may oscillate because of numerical instability which occurs due to the indefiniteness, when bearings more than one approach to the identical value. The oscillation makes the condition for terminating iterations complex. This paper proposes a technique for avoiding the indefiniteness in ML criteria.

• Journal of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.127-147
• /
• 2019

In this paper we establish some new explicit solutions for impulsive linear fractional differential equations with impulses at fixed times, which provides a handy tool in deriving singular integral-sum inequalities and an impulsive fractional comparison principle. Thus we study the Mittag-Leffler stability of impulsive differential equations with the Caputo fractional derivative by using the impulsive fractional comparison principle and piecewise continuous functions of Lyapunov's method. Also, we give some examples to illustrate our results.

• Structural Engineering and Mechanics
• /
• v.27 no.5
• /
• pp.609-623
• /
• 2007

The problem of a semi-infinite magneto-electro-elastically impermeable mode-III crack in a magneto-electro-elastic material is considered under the action of impact loads. For the case when a pair of concentrated anti-plane shear impacts, electric displacement and magnetic induction impacts are exerted symmetrically on the upper and lower surfaces of the crack, the magneto-electro-elastic field ahead of the crack tip is determined in explicit form. The dynamic intensity factors and dynamic energy density factor are obtained. The method adopted is to reduce the mixed initial-boundary value problem, by using the Laplace and Fourier transforms, into three simultaneous dual integral equations, one of which is converted into an Abel's integral equation and the others into a singular integral equation with Cauchy kernel. Based on the obtained fundamental solutions of point impact loads, the solutions of two kinds of different loading cases are evaluated by integration. For some particular cases, the present results reduce to the previous results.

• The Transactions of the Korean Institute of Electrical Engineers
• /
• v.40 no.3
• /
• pp.243-249
• /
• 1991

Adaptive mesh refinement scheme is incorporated with the boundary element analysis in order to get accurate solution with relatively fewer unnowns for magnetostatic field analysis. A new andsimple posteriori local error estimate is also presented. The local error is defined as an integraktion over the element of the difference between solutions from quadratic interpolation functions and linear interpolation functions and is used as the criterion for mesh refinement. Case study with a singular point reveals that adaptive meshes are more efficient in accuracy of solutions than uniform meshs generated by dividing al the elements evenly. The adaptive meshes give much better rate of convergence in global errors than the uniform meshes.

• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.51-67
• /
• 2004

A matrix pair $(X_0,\;Y_0)$ is called a Hermitian nonnegative-definite(respectively, positive-definite) solution to the matrix equation $GXG^*\;+\;HYH^*\;=\;C$ with unknown X and Y if $X_{0}$ and $Y_{0}$ are Hermitian nonnegative-definite (respectively, positive-definite) and satisfy $GX_0G^*\;+\;HY_0H^*\;=\;C$. Necessary and sufficient conditions for the existence of at least a Hermitian nonnegative-definite (respectively, positive-definite) solution to the matrix equation are investigated. A representation of the general Hermitian nonnegative-definite (respectively positive-definite) solution to the equation is also obtained when it has such solutions. Two presented examples show these advantages of the proposed approach.