• Journal of Institute of Control, Robotics and Systems
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• v.11 no.11
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• pp.895-900
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• 2005

We derive a linear matrix inequality(LMI) condition guaranteeing that any invariant zeros of a triple (A, B, C) lie in the open left half plane of the complex plane, i.e. $C(sI-A)^{-1}B$ is minimum phase. The LMI condition is equivalent to a certain constrained Lyapunov matrix equation which can be found in many results relating to stability analysis or control design. We show that the LMI condition can be used to simplify various control engineering problems such as a dynamic output feedback control problem, a variable structure static output feedback control problem, and a nonlinear system observer design problem. Finally, we give some numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 2001.10a
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• pp.121.2-121
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• 2001

Many of today´s robot are required to perform tasks which demand a high level of accuracy in end-effector positioning. Those rigid robots are very inefficient and slow because its have large and heavy links, In an attempt to solve these problems, a robots using flexible beam were created. But the single-link flexible beam is infinite-dimensional system. Many researchers have proposed controlling such a beam an approximated model consisting of a finite a number of models. In this paper, we start by deriving the analytic model for the dynamics of general single-link beam, and a controller is designed for flexible beam with integral type servo system bases of the linear matrix inequality (LM) technique. To the end, simulation results show that a designed controller guarantees affective vibration control the single-link flexible beam.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.465-478
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• 2006

In this paper, we introduce a new class of completely generalized strongly nonlinear quasivariational inequalities and establish its equivalence with a class of fixed point problems by using the resolvent operator technique. Utilizing this equivalence, we develop a three-step iterative scheme with errors, obtain a few existence theorems of solutions for the completely generalized non-linear strongly quasivariational inequality involving relaxed monotone, relaxed Lipschitz, strongly monotone and generalized pseudocontractive mappings and prove some convergence and stability results of the sequence generated by the three-step iterative scheme with errors. Our results include several previously known results as special cases.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.877-888
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• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.297-302
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• 2014

A well known result due to Ankeny and Rivlin [1] states that if $p(z)={\sum}^n_{j=0}a_jz^j$ is a polynomial of degree n satisfying $p(z){\neq}0$ for |z| < 1, then for $R{\geq}1$ $$\max_{{\mid}z{\mid}=R}{\mid}p(z){\mid}{\leq}{\frac{R^n+1}{2}}\max_{{\mid}z{\mid}=1}{\mid}p(z){\mid}$$. It was proposed by Professor R.P. Boas Jr. to obtain an inequality analogous to this inequality for polynomials having no zeros in |z| < k, k > 0. In this paper, we obtain some results in this direction, by considering polynomials of degree $n{\geq}2$, having all its zeros on the disk |z| = k, $k{\leq}1$.

• 전기의세계
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• v.30 no.6
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• pp.375-385
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• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• Journal of Power Electronics
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• v.11 no.3
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• pp.327-334
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• 2011

Single-phase power factor correction (PFC) converter circuits are non-linear systems due to the contribution of their multiplier. This non-linearity causes difficulties in analysis and design. Models that reduce the system to a linear system involve considerable approximation, and produce results that are susceptible to instability problems. In this paper a piecewise affine (PWA) system is introduced for describing the nonlinear averaged model. Then robust output feedback controllers are established in terms of the linear matrix inequality (LMI). Simulation and experiments results show the effectiveness of the proposed control method.

• Korean Journal of Mathematics
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• v.31 no.1
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• pp.109-120
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• 2023

The Berezin symbol à of an operator A on the reproducing kernel Hilbert space 𝓗 (Ω) over some set Ω with the reproducing kernel k_λ is defined by $${\tilde{A}}(\lambda)=\,\;{\lambda}{\in}{\Omega}$$. The Berezin number of an operator A is defined by $$ber(A):=\sup_{{\lambda}{\in}{\Omega}}{\mid}{\tilde{A}}({\lambda}){\mid}$$. We study some problems of operator theory by using this bounded function Ã, including estimates for Berezin numbers of some operators, including truncated Toeplitz operators. We also prove an operator analog of some Young inequality and use it in proving of some inequalities for Berezin number of operators including the inequality ber (AB) ≤ ber (A) ber (B), for some operators A and B on 𝓗 (Ω). Moreover, we give in terms of the Berezin number a necessary condition for hyponormality of some operators.

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.497-520
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• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).

• Journal of Preventive Medicine and Public Health
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• v.42 no.5
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• pp.275-282
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• 2009

Objectives : This study aimed to verify the association between wealth or income level and health status after adjusting for other socio-economic position (SEP) indicators among Korean adults aged 45 and over. Methods : Data were obtained from the 1st wave of Korean Longitudinal Study of Ageing (households: 6,171, persons: 10,254). We used self-rated health status and activities of daily living (ADLs) as dependent variables. Explanatory variables included both net wealth measured by savings, immovables, the other valuated assets and total income including pay, transfer, property and so on. Binary logistic regression was conducted to examine the relationships. Also, in order to determine the relative health inequality across economic groups, we estimated the relative index of inequality (RII). Results : The inequality of health status was evident among various wealth and income groups. The wealthiest group (5th quintile) was much healthier than the poorest group, and this differential increased with age. Likewise, higher income was associated with better health status among the elderly. However, these effects, as measured by the odds ratio and RII, showed that wealth was more important in determining health status of elderly people. Conclusions : This study suggests that economic capability plays a significant role in determining the health status and other health-related problems among the elderly. Particularly, our results show that health status of the aged is related more closely to the individual s wealth than income.