• 전자공학회논문지SC
• /
• 제48권5호
• /
• pp.59-65
• /
• 2011

본 논문에서는 폴리토픽 불확실성을 가지는 이산시간 변수종속 특이시스템에 대한 저차(low order)의 변수종속 차수축소 강인 $H_{\infty}$ 필터 설계기법을 제안한다. 먼저, 변수종속 특이시스템에 대한 유계 실수정리(bounded real lemma)를 변수종속 리아푸노프 (Lyapunov) 함수로부터 유도한다. 유계 실수정리로부터 폴리토픽 기법과 새로운 차수축소 기법을 이용하여 저차의 강인 $H_{\infty}$ 필터 설계방법을 볼록최적화가 가능한 선형행렬부등식 접근방법을 이용하여 제시한다. 따라서 제안하는 변수종속 차수축소 강인 $H_{\infty}$ 필터 설계방법은 미리 정한 차수의 $H_{\infty}$ 필터를 제공한다. 수치예제를 통하여 제시한 저차의 필터 설계방법의 타당성을 보인다.

• East Asian mathematical journal
• /
• 제36권5호
• /
• pp.583-591
• /
• 2020

In [8, 9] they introduced a new finite element method for accurate numerical solutions of Poisson equations with corner singularities. They consider the Poisson equations with corner singularities, compute the finite element solutions using standard Finite Element Methods and use the extraction formula to compute the stress intensity factor(s), then they posed new PDE with a regular solution by imposing the nonhomogeneous boundary condition using the computed stress intensity factor(s), which converges with optimal speed. From the solution they could get an accurate solution just by adding the singular part. The error analysis was given in [5]. In their approaches, the singular functions and the extraction formula which give the stress intensity factor are the basic elements. In this paper we consider the biharmonic problems with the cramped and/or simply supported boundary conditions and get the singular functions and its duals and find properties of them, which are the cornerstones of the approaches of [8, 9, 10].

• International Journal of Computer Science & Network Security
• /
• 제21권12호
• /
• pp.223-227
• /
• 2021

A treatment based on the algebraic operations on fuzzy numbers is used to replace the fuzzy problem into an equivalent crisp one. The finite difference technique is used to replace the continuous boundary value problem (BVP) of arbitrary order 1<α≤2, with fuzzy boundary parameters into an equivalent crisp (algebraic or differential) system. Three numerical examples with different behaviors are considered to illustrate the treatment of the singular perturbed case with different fractional orders of the BVP (α=1.8, α=1.9) as well as the classical second order (α=2). The calculated fuzzy solutions are compared with the crisp solutions of the singular perturbed BVP using triangular membership function (r-cut representation in parametric form) for different values of the singular perturbed parameter (ε=0.8, ε=0.9, ε=1.0). Results are illustrated graphically for the different values of the included parameters.

• 한국정밀공학회지
• /
• 제14권1호
• /
• pp.194-204
• /
• 1997

In this paper, we consider the rational approximation of multiple input delay systems. The method of computing Hankel singular values and vectors is firstly introduced, where explicitly shows the structure of the corresponding Hankel singular vectors. Secondly, rational approximants are obtained from output nor- mal relizations, which are constructed by Hankel singular values and vectors. As a result, it is shown that rational approximants by output normal realization preserve intrinsic properties of time delay systems than Pad'e approximants.

• East Asian mathematical journal
• /
• 제31권5호
• /
• pp.635-652
• /
• 2015

It is shown that for a general Haar shift operator, and a weight in the $A_2$ weight class, we establish the weighted norm estimate which linearly depends on $A_2$-characteristic $[w]_{A_2}$. Although the result is now well known, we introduce the new method, which is called the iterated Bellman function method, to provide the estimate.

• International Journal of Control, Automation, and Systems
• /
• 제4권1호
• /
• pp.124-135
• /
• 2006

In this paper, we propose a switching control method for a class of 2nd order nonlinear systems with single input. The main idea is to switch the control law before the trajectory of the solution arrives at singular hyperplanes which are defined by the denominator of the control law. The proposed method can handle a class of nonlinear systems which is difficult to be stabilized by the existing methods such as feedback linearization, backstepping, control Lyapunov function, and sliding mode control.

• 전기학회논문지
• /
• 제57권8호
• /
• pp.1429-1433
• /
• 2008

In this paper, we consider the design method of robust guaranteed cost controller for discrete-time singular systems with norm-bounded time-varying parameter uncertainty. In order to get the optimum(minimum) value of guaranteed cost, an optimization problem is given by linear matrix inequality (LMI) approach. The sufficient condition for the existence of controller and the upper bound of guaranteed cost function are proposed in terms of strict LMIs without decompositions of system matrices. Numerical examples are provided to show the validity of the presented method.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제13권1호
• /
• pp.758-771
• /
• 2021

This paper presents a novel control scheme for the three-dimensional (3D) path following of underactuated Autonomous Underwater Vehicle (AUVs) subject to unknown internal and external disturbances, in term of the time scale decomposition method. As illustration, two-time scale motions are first artificially forced into the closed-loop control system, by appropriately selecting the control gain of the integrator. Using the singular perturbation theory, the integrator is considered as a fast dynamical control law that designed to shape the space configuration of fast variable. And then the stabilizing controller is designed in the reduced model independently, based on the time scale decomposition method, leading to a relatively simple control law. The stability of the resultant closed-loop system is demonstrated by constructing a composite Lyapunov function. Finally, simulation results are provided to prove the efficacy of the proposed controller for path following of underactuated AUVs under internal and external disturbances.

• 한국전산구조공학회논문집
• /
• 제23권1호
• /
• pp.1-8
• /
• 2010

푸리에 급수는 사인 곡선처럼 일정한 진폭으로 진동하는 정규파(wave)를 사용한다. 그래서 푸리에 급수에서 사용하는 함수는 진동수의 크기가 시간에 따라 변하지 않기 때문에 국부적인 영역에서 급작스런 진동이나 불연속성을 갖는 신호를 표현하기에는 한계가 있다. 그러나 이러한 푸리에 해석의 단점을 여러개의 적절한 웨이블렛의 선형조합에 의해 보완할 수 있는 것이 웨이블렛 급수해석이다. 시간에 집중되어진 궤적의 작은 잔파(wavelet)를 사용함으로써 시간과 주기의 폭을 변화시킬 수 있기 때문에 유동적이고, 특이(singular)형상을 지닌 신호들을 보다 효율적으로 표현할 수 있다. 이 연구의 주요 목적은 웨이블렛 급수해석이라고 불리는 방법을 2계 편미분방정식으로 표현되는 1차원 축방향 부재에 웨이블렛 이론을 적용함과 동시에 유한요소법과 같은 수치해석법과의 비교를 통해 성능평가를 위해 제안되었다. 여러 형태의 웨이블렛 함수의 검토 후에 HAT 함수가 웨이블렛 및 스케일링 함수로 채택되었다. 등분포하중을 받는 경우의 축방향 부재해석에서 제안된 방법은 유한요소법과 같이 효율적임을 보이며, 특히 응력특이점에서는 더 정확한 값을 보였으며, 계산시간도 절약되는 장점을 얻을 수 있었다.

• East Asian mathematical journal
• /
• 제39권3호
• /
• pp.355-367
• /
• 2023

Extending [14], we establish the existence of multiple positive solutions for a Schrödinger-type singular elliptic equation: $$\{{-{\Delta}u+V(x)u={\lambda}{\frac{f(u)}{u^{\beta}}},\;x{\in}{\Omega}, \atop u=0,\;x{\in}{\partial}{\Omega},$$ where 0 ∈ Ω is a bounded domain in ℝ^N, N ≥ 1, with a smooth boundary ∂Ω, β ∈ [0, 1), f ∈ C[0, ∞), V : Ω → ℝ is a bounded function and λ is a positive parameter. In particular, when f(s) > 0 on [0, σ) and f(s) < 0 for s > σ, we establish the existence of at least three positive solutions for a certain range of λ by using the method of sub and supersolutions.