• Title/Summary/Keyword: Differential inequality

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Robust $H^{\infty}$ control for parameter uncertain time-varying systems with time-varying delays in state and control input (파라미터 불확실성 시변 시간지연 시스템에 대한 견실 $H^{\infty}$ 제어)

  • 김기태;김종해;박홍배
    • 제어로봇시스템학회:학술대회논문집
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    • 1997.10a
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    • pp.113-116
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    • 1997
  • In this paper, we present a robust $H^{\infty}$ controller design method for parameter uncertain time-varying systems with disturbance and that have time-varying delays in both state and control. It is found that the problem shares the same formulation with the $H^{\infty}$ control problem for systems without uncertainty. Through a certain differential Riccati inequality approach, a class of stabilizing continuous controller is proposed. For parameter uncertainties, disturbance and time varying delays, proposed controllers the plant and guarantee an $H^{\infty}$ norm bound constraint on disturbance attenuation for all admissible uncertainties. Finally a numerical example is given to demonstrate the validity of the results.ts.

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BEST CONSTANT IN ZYGMUND'S INEQUALITY AND RELATED ESTIMATES FOR ORTHOGONAL HARMONIC FUNCTIONS AND MARTINGALES

  • Osekowski, Adam
    • Journal of the Korean Mathematical Society
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    • v.49 no.3
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    • pp.659-670
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    • 2012
  • For any $K$ > $2/{\pi}$ we determine the optimal constant $L(K)$ for which the following holds. If $u$, $tilde{u}$ are conjugate harmonic functions on the unit disc with $\tilde{u}(0)=0$, then $$ {\int}_{-\pi}^{\pi}{\mid}\tilde{u}(e^{i\phi}){\mid}\frac{d{\phi}}{2{\pi}}{\leq}K{\int}_{-\pi}^{\pi}{\mid}u(e^{i{\phi}}){\mid}{\log}^+{\mid}u(e^{i{\phi}}){\mid}\frac{d{\phi}}{2{\pi}}+L(K).$$ We also establish a related estimate for orthogonal harmonic functions given on Euclidean domains as well as an extension concerning orthogonal martingales under differential subordination.

A New Constraint Handling Method for Economic Dispatch

  • Li, Xueping;Xiao, Canwei;Lu, Zhigang
    • Journal of Electrical Engineering and Technology
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    • v.13 no.3
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    • pp.1099-1109
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    • 2018
  • For practical consideration, economic dispatch (ED) problems in power system have non-smooth cost functions with equality and inequality constraints that makes the problems complex constrained nonlinear optimization problems. This paper proposes a new constraint handling method for equality and inequality constraints which is employed to solve ED problems, where the incremental rate is employed to enhance the modification process. In order to prove the applicability of the proposed method, the study cases are tested based on the classical particle swarm optimization (PSO) and differential evolution (DE) algorithm. The proposed method is evaluated for ED problems using six different test systems: 6-, 15-, 20-, 38-, 110- and 140-generators system. Simulation results show that it can always find the satisfactory solutions while satisfying the constraints.

GLOBAL STABILITY ANALYSIS FOR A CLASS OF COHEN-GROSSBERG NEURAL NETWORK MODELS

  • Guo, Yingxin
    • Bulletin of the Korean Mathematical Society
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    • v.49 no.6
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    • pp.1193-1198
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    • 2012
  • By constructing suitable Lyapunov functionals and combining with matrix inequality technique, a new simple sufficient condition is presented for the global asymptotic stability of the Cohen-Grossberg neural network models. The condition contains and improves some of the previous results in the earlier references.

CONTROLLABILITY FOR NONLINEAR VARIATIONAL EVOLUTION INEQUALITIES

  • Park, Jong-Yeoul;Jeong, Jin-Mun;Rho, Hyun-Hee
    • Journal of the Korean Mathematical Society
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    • v.49 no.5
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    • pp.881-891
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    • 2012
  • In this paper we investigate the approximate controllability for the following nonlinear functional differential control problem: $$x^{\prime}(t)+Ax(t)+{\partial}{\phi}(x(t)){\ni}f(t,x(t))+h(t)$$ which is governed by the variational inequality problem with nonlinear terms.

On Opial Type Inequalities with Nonlocal Conditions and Applications

  • Bougoffa, Lazhar;Daoud, Jamal Ibrahim
    • Kyungpook Mathematical Journal
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    • v.51 no.2
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    • pp.165-175
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    • 2011
  • The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.

ON OPIAL-TYPE INEQUALITIES VIA A NEW GENERALIZED INTEGRAL OPERATOR

  • Farid, Ghulam;Mehboob, Yasir
    • Korean Journal of Mathematics
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    • v.29 no.2
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    • pp.227-237
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    • 2021
  • Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

EXISTENCE RESULTS FOR BOUNDARY VALUE PROBLEMS OF VOLTERRA-FREDHOLM SYSTEM INVOLVING CAPUTO DERIVATIVE

  • Shakir M. Atshan;Ahmed A. Hamoud
    • Nonlinear Functional Analysis and Applications
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    • v.29 no.2
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    • pp.545-558
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    • 2024
  • In this study, a class of nonlinear boundary fractional Caputo Volterra-Fredholm integro-differential equations (CV-FIDEs) is taken into account. Under specific assumptions about the available data, we firstly demonstrate the existence and uniqueness features of the solution. The Gronwall's inequality, a adequate singular Hölder's inequality, and the fixed point theorem using an a priori estimate procedure. Finally, a case study is provided to highlight the findings.

Differential Effects of Family Income on Self-rated Health by Age: Analysis of Seoul Citizens Health Indicators Survey 2001, 2005 (소득수준이 주관적 건강상태에 미치는 영향의 연령대별 차이: 2001, 2005년 서울시민보건지표조사 자료의 분석 결과)

  • Jung, Youn;Oh, Ju-Hwan;Cho, Young-Tae
    • Journal of Preventive Medicine and Public Health
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    • v.40 no.5
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    • pp.381-387
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    • 2007
  • Objectives: This study was conducted in order to determine how the association between socioeconomic position(SEP) and health status changes with age among Seoul residents aged 25 and over. Methods: We utilized the 2001 and 2005 Seoul Citizens Health Indicators Surveys. We used self-rated 'poor' health status as an outcome variable, and family income as an indicator of SEP. In order to characterize the differential effects of socioeconomic position on health by age, we conducted separate multivariate analyses by 10-year age groups, controlling for sociodemographic covariates. In order to assess the relative health inequality across socioeconomic groups, we estimated the Relative Index of Inequality (RII). Results: The risk of 'poor health' is significantly high in low family income groups, and this increased risk is seen at all ages. However, the magnitude of relative socioeconomic inequality in health, as measured by the odds ratio and RII, is not identical across age groups. The difference in health across income groups is small in early adulthood (ages 25-34), but increases with age until relatively late in life (ages 35-64). It then decreases among the elderly population (ages more than 65). When the RII reported in 2005 is compared to that reported in 2001, RII can be seen to have increased across all ages, with the exception of individuals aged 25-34. Conclusions: The magnitude of health inequality is the greatest during mid- to late adulthood (ages 45-64). In addition, health inequalities have worsened between 2001 and 2005 across all age groups after economic crisis.