• Title, Summary, Keyword: global stability

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EXISTENCE AND LONG-TIME BEHAVIOR OF SOLUTIONS TO NAVIER-STOKES-VOIGT EQUATIONS WITH INFINITE DELAY

  • Anh, Cung The;Thanh, Dang Thi Phuong
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.2
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    • pp.379-403
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    • 2018
  • In this paper we study the first initial boundary value problem for the 3D Navier-Stokes-Voigt equations with infinite delay. First, we prove the existence and uniqueness of weak solutions to the problem by combining the Galerkin method and the energy method. Then we prove the existence of a compact global attractor for the continuous semigroup associated to the problem. Finally, we study the existence and exponential stability of stationary solutions.

QUALITATIVE ANALYSIS OF A GENERAL PERIODIC SYSTEM

  • Xu, Shihe
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.1039-1048
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    • 2018
  • In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

ASYMPTOTIC STABILIZATION FOR A DISPERSIVE-DISSIPATIVE EQUATION WITH TIME-DEPENDENT DAMPING TERMS

  • Yi, Su-Cheol
    • Journal of the Chungcheong Mathematical Society
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    • v.33 no.4
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    • pp.445-468
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    • 2020
  • A long-time behavior of global solutions for a dispersive-dissipative equation with time-dependent damping terms is investigated under null Dirichlet boundary condition. By virtue of an appropriate new Lyapunov function and the Lojasiewicz-Simon inequality, we show that any global bounded solution converges to a steady state and get the rate of convergence as well, when damping coefficients are integrally positive and positive-negative, respectively. Moreover, under the assumptions on on-off or sign-changing damping, we derive an asymptotic stability of solutions.

Synthesis and Evaluation of Thermo-stable Organic Solderability Preservatives Based Upon Poly(vinyl pyridine-co-methylmethacrylate) (폴리(비닐피리딘-co-메틸메타아크릴레이트) 기반 열안정성 유기솔더보존제의 합성 및 평가)

  • Bui, Tien Van;Choi, Ho-Suk;Seo, Chung-Hee;Jang, Young-Sic;Heo, Ik-Sang
    • Korean Chemical Engineering Research
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    • v.49 no.2
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    • pp.161-167
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    • 2011
  • Recent popularity in mobile electronics requires higher standard on the mechanical strength of electronic packaging. Thus, the method of soldering between chip and substrate in electronic packaging process is changing from conventional method using intermetallic compound to a new method using organic solderability preservatives (OSP) in order to improve the stability and the reliability of final product. Since current OSPs have several serious problems like thermo-stability during packaging process, however, it is necessary to develop new OSPs having thermo-stability. The main purpose of this study is to develop various thermo-stable OSPs based upon poly(vinyl pyridine-co- methylmethacrylate) and to evaluate their anti-oxidation property protecting Cu pad, thermo-stability and solubility to acid- or alcohol-containing aqueous solution during pos-fluxing. All OSPs showed not only good anti-oxidation property, thermo-stability and solubility but also more advantages like low cost, less odor, and less hygroscopic.

A New Design Method for T-S Fuzzy Controller with Pole Placement Constraints

  • Joh, Joongseon;Jeung, Eun-Tae;Chung, Won-Jee;Kwon, Sung-Ha
    • Journal of the Korean Institute of Intelligent Systems
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    • v.7 no.3
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    • pp.72-80
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    • 1997
  • A new design method for Takagi-Sugeno (T-S in short) fuzzy controller which guarantees global asymptotic stability and satisfies a desired performance is proposed in this paper. The method uses LMI(Linear Matrix Inequality) approach to find the common symmetric positive definite matrix P and feedback fains K/sub i/, i= 1, 2,..., r, numerically. The LMIs for stability criterion which treats P and K'/sub i/s as matrix variables is derived from Wang et al.'s stability criterion. Wang et al.'s stability criterion is nonlinear MIs since P and K'/sub i/s are coupled together. The desired performance is represented as $ LMIs which place the closed-loop poles of $ local subsystems within the desired region in s-plane. By solving the stability LMIs and pole placement constraint LMIs simultaneously, the feedback gains K'/sub i/s which gurarntee global asymptotic stability and satisfy the desired performance are determined. The design method is verified by designing a T-S fuzzy controller for an inverted pendulum with a cart using the proposed method.

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An Empirical Study on User Acceptance of Micro e-Payment Systems : System Features, Transaction Cost, and Provider (소액 전자결제시스템 수용의지에 관한 실증연구 : 시스템 특성, 거래비용과 제공업체를 중심으로)

  • Chung, Suk-Kyun;Ryoo, Chang-Wan;Ku, Tae-Yong
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.33 no.4
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    • pp.130-137
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    • 2010
  • This paper analyzes the main factors affecting user selection of a small-sum electronic payment system using survey data of 396 users. Several findings emerge. First, users consider three pillars and eight factors in adopting a new system : system features(stability, security, and flexibility), transaction cost(payment commission and settlement period), and financial capability of provider(stability of financial structure, risk management capability, and funding capability). Second, the stability of the financial structure of the system provider is the most important factor to user acceptance of a new e-payment system. Users tend to consider uncertainty risk more seriously than transaction cost. This reflects the reality that electronic payment system service industry has not fully fledged yet. Third, some moderating effects exist according to payment methods and business usages. As for payment methods, speedy settlement cycle for wired/wireless phone payment, system stability for credit card and account transfer payment, and security for advance payment means are crucial factors. As for business usages, the stability of financial structure for online game content, system stability for music and video content, proxy payment commission for e-learning content, flexibility of the payment system for digital adult content, and security for public services are decisive ones.

Determinants of Sukuk Market Development: Macroeconomic Stability and Institutional Approach

  • BASYARIAH, Nuhbatul;KUSUMA, Hadri;QIZAM, Ibnu
    • The Journal of Asian Finance, Economics and Business
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    • v.8 no.2
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    • pp.201-211
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    • 2021
  • This study aims to analyze the determinants of macroeconomic and institutional stability on the development of the global sukuk market by controlling the effects of population. This study uses panel data namely GDP per-capita, exchange rate, and inflation as the proxies for macroeconomic stability sourced from the World Development Index, and six dimensions of Worldwide Governance Indicators (WGI) as institutional proxies sourced from WGI-World Bank. To make robust the relationship between macroeconomics and institutional on the global sukuk market, the population (POP) variable was included as a control variable. The development of sukuk uses a proxy for sukuk issuance in the International Islamic Financial Market, for the annual period from 2002-2017. The data was analyzed using the General Method of Moment, and the results show that by controlling the population effects that proved to be significant, GDP per-capita and the rule of law have a significant impact on the development of sukuk, especially when incorporating population effects as control variables, whereby further ascertaining the effect of each macroeconomic-stability variable and institutional stability on sukuk development, especially inflation, found not to affect sukuk development. These results also confirm the previous findings, whereby inflation remains controllable at a certain level for economic development.

Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design

  • Rasappan, Suresh;Vaidyanathan, Sundarapandian
    • Kyungpook Mathematical Journal
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    • v.54 no.2
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    • pp.293-320
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    • 2014
  • In this paper, global chaos synchronization is investigated for WINDMI (J. C. Sprott, 2003) and Coullet (P. Coullet et al, 1979) chaotic systems using adaptive backstepping control design based on recursive feedback control. Our theorems on synchronization for WINDMI and Coullet chaotic systems are established using Lyapunov stability theory. The adaptive backstepping control links the choice of Lyapunov function with the design of a controller and guarantees global stability performance of strict-feedback chaotic systems. The adaptive backstepping control maintains the parameter vector at a predetermined desired value. The adaptive backstepping control method is effective and convenient to synchronize and estimate the parameters of the chaotic systems. Mainly, this technique gives the flexibility to construct a control law and estimate the parameter values. Numerical simulations are also given to illustrate and validate the synchronization results derived in this paper.

Nonlinear Attitude Control for Uncertain Quad-rotors Using a Global Approximation-Free Control Scheme (GAFC 비선형 제어기법을 적용한 쿼드로터의 자세 및 고도제어)

  • Kim, Young-Ouk;Park, Seong-Yong;Leeghim, Henzeh
    • Journal of Institute of Control, Robotics and Systems
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    • v.22 no.10
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    • pp.779-787
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    • 2016
  • A nonlinear control law for the quad-rotor of a low-complexity, global approximation-free from system uncertainties and external disturbances are described in this paper. The control law guarantees convergence to a small bounded error using a prescribed performance function. The stability of the proposed nonlinear control system is also proven by the Lyapunov stability theorem. The advantage of this technique is that it has a simpler form than any other nonlinear compensators and is applicable to any nonlinear systems without precise knowledge of the systems. In this paper, the proposed approach is applied to attitude/altitude control of a quad-rotor. Numerical simulations are performed to investigate the proposed nonlinear attitude control law by applying it to an uncertain quadcopter system with external disturbances.

STABILITY ANALYSIS OF A HOST-VECTOR TRANSMISSION MODEL FOR PINE WILT DISEASE WITH ASYMPTOMATIC CARRIER TREES

  • Lashari, Abid Ali;Lee, Kwang Sung
    • Journal of the Korean Mathematical Society
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    • v.54 no.3
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    • pp.987-997
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    • 2017
  • A deterministic model for the spread of pine wilt disease with asymptomatic carrier trees in the host pine population is designed and rigorously analyzed. We have taken four different classes for the trees, namely susceptible, exposed, asymptomatic carrier and infected, and two different classes for the vector population, namely susceptible and infected. A complete global analysis of the model is given, which reveals that the global dynamics of the disease is completely determined by the associated basic reproduction number, denoted by $\mathcal{R}_0$. If $\mathcal{R}_0$ is less than one, the disease-free equilibrium is globally asymptotically stable, and in such a case, the endemic equilibrium does not exist. If $\mathcal{R}_0$ is greater than one, the disease persists and the unique endemic equilibrium is globally asymptotically stable.