• Title/Summary/Keyword: Boundedness

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SLICE REGULAR BESOV SPACES OF HYPERHOLOMORPHIC FUNCTIONS AND COMPOSITION OPERATORS

  • Kumar, Sanjay;Manzoor, Khalid
    • Communications of the Korean Mathematical Society
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    • v.36 no.4
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    • pp.651-669
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    • 2021
  • In this paper, we investigate some basic results on the slice regular Besov spaces of hyperholomorphic functions on the unit ball 𝔹. We also characterize the boundedness, compactness and find the essential norm estimates for composition operators between these spaces.

Uniform ultimate boundedness of control systems with matched and mismatched uncertainties by Lyapunov-like method

  • Sung, Yulwan;Shibata, Hiroshi;Park, Chang-Young;Kwo, Oh-Kyu
    • 제어로봇시스템학회:학술대회논문집
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    • 1996.10a
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    • pp.119-122
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    • 1996
  • The recently proposed control method using a Lyapunov-like function can give global asymptotic stability to a system with mismatched uncertainties if the uncertainties are bounded by a known function and the uncontrolled system is locally and asymptotically stable. In this paper, we modify the method so that it can be applied to a system not satisfying the latter condition without deteriorating qualitative performance. The assured stability in this case is uniform ultimate boundedness which is as useful as global asymptotic stability in the sense that it is global and the bound can be taken arbitrarily small. By the proposed control law we can deal with both matched and mismatched uncertain systems. The above facts conclude that Lyapunov-like control method is superior to any other Lyapunov direct methods in its applicability to uncertain systems.

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SOLVABILITY AND BOUNDEDNESS FOR GENERAL VARIATIONAL INEQUALITY PROBLEMS

  • Luo, Gui-Mei
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.2
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    • pp.589-599
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    • 2013
  • In this paper, we propose a sufficient condition for the existence of solutions to general variational inequality problems (GVI(K, F, $g$)). The condition is also necessary when F is a $g-P^M_*$ function. We also investigate the boundedness of the solution set of (GVI(K, F, $g$)). Furthermore, we show that when F is norm-coercive, the general complementarity problems (GCP(K, F, $g$)) has a nonempty compact solution set. Finally, we establish some existence theorems for (GNCP(K, F, $g$)).

Robust Direct Adaptive Fuzzy Controller (강인한 직접 적응 퍼지 제어기)

  • 김용태;변증남
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1997.10a
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    • pp.199-203
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    • 1997
  • In this paper is proposed a new direct adaptive fuzzy controller that dan ve applied for tracking control of a class of uncertain nonlinear SISO systems. It is shown that, in the presence of the perturbations such as fuzzy approximation error and external disturbance, boundedness of all the signals in the system is ensured, while under the assumption of no perturbations, the stability of the overall system in guaranteed. Also, the concept of persistent excitation in the adaptive fuzzy control systems is introduced to guarantee the convergence and the boundedness of adaptation parameter in the proposed controllers. Simulation example shows the effectiveness of the proposed method in the presence of fuzzy approximation error and external disturbance.

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Uniform ultimate boundedness and global asympotic stabilization for systems with mis-matched uncertainties (비 매칭 불확실성이 있는 비선형시스템의 균일 종국적 유계성 및 대역적 점근 안정성)

  • 장충환;성열완;이건일
    • Journal of the Korean Institute of Telematics and Electronics S
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    • v.35S no.7
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    • pp.29-36
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    • 1998
  • In this paper we propose a control law using a Lyapunov-like function that makes stable the systems which have mis-matched uncertainties. The existing control law using a Lyapunov-like function, which gives global saymptotic stability, is designed under the assumption of a targetsystem to be stable locally. But we broaden here the class of target systems by designing the control law which can give uniform ultimate boundedness to even the systems not satisfing the locally asymptotic stability. And we also show that the control law giving global asymptotic stability can be designed more systematically through using the uniform ultimate boundedness.

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Weighted LP Estimates for a Rough Maximal Operator

  • Al-Qassem, H.M.
    • Kyungpook Mathematical Journal
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    • v.45 no.2
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    • pp.255-272
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    • 2005
  • This paper is concerned with studying the weighted $L^P$ boundedness of a class of maximal operators related to homogeneous singular integrals with rough kernels. We obtain appropriate weighted $L^P$ bounds for such maximal operators. Our results are extensions and improvements of the main theorems in [2] and [5].

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BOUNDEDNESS FOR PERTURBED DIFFERENTIAL EQUATIONS VIA LYAPUNOV EXPONENTS

  • Choi, Sung Kyu;Kim, Jiheun;Koo, Namjip;Ryu, Chunmi
    • Journal of the Chungcheong Mathematical Society
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    • v.25 no.3
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    • pp.589-597
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    • 2012
  • In this paper we investigate the stability of solutions of the perturbed differential equations with the positive order of the perturbation by using the notion of the Lyapunov exponent of unperturbed equations and an integral inequality of Bihari type.

A NOTE ON TWO WEIGHT INEQUALITIES FOR THE DYADIC PARAPRODUCT

  • Chung, Daewon
    • East Asian mathematical journal
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    • v.36 no.3
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    • pp.377-387
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    • 2020
  • In this paper, we provide detailed proof of the Sawyer type characterization of the two weight estimate for the dyadic paraproduct. Although the dyadic paraproduct is known to be a well localized operators and the testing conditions obtained from checking boundedness of the given localized operator on a collection of test functions are provided by many authors. The main purpose of this paper is to present the necessary and sufficient conditions on the weights to ensure boundedness of the dyadic paraproduct directly.