• Title/Summary/Keyword: Lyapunov Function

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On the stabilization of singular bilinear systems

  • Liang, Jia-Rong;Choi, Ho-Lim;Lim, Jong-Tae
    • 제어로봇시스템학회:학술대회논문집
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    • 2003.10a
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    • pp.449-451
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    • 2003
  • In this paper, the stability problem for singular bilinear system is investigated. We present state feedback control laws for two classes of singular bilinear plants. Asymptotic stability of the closed-loop systems is derived by employing singular Lyapunov's direct method. The primary advantage of our approach lies in its simplicity. In order to verify effectiveness of the results, two numerical examples are given.

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Robust Digital Nonlinear Friction Compensation - Theory (견실한 비선형 마찰보상 이산제어 - 이론)

  • 강민식;김창제
    • Journal of the Korean Society for Precision Engineering
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    • v.14 no.4
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    • pp.88-96
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    • 1997
  • This paper suggests a new non-linear friction compensation for digital control systems. This control adopts a hysteresis nonlinear element which can introduce the phase lead of the control system to compensate the phase delay comes from the inherent time delay of a digital control. A proper Lyapunov function is selected and the Lyapunov direct method is used to prove the asymptotic stability of the suggested control.

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STABILITY OF FRACTIONAL-ORDER NONLINEAR SYSTEMS DEPENDING ON A PARAMETER

  • Ben Makhlouf, Abdellatif;Hammami, Mohamed Ali;Sioud, Khaled
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.4
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    • pp.1309-1321
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    • 2017
  • In this paper, we present a practical Mittag Leffler stability for fractional-order nonlinear systems depending on a parameter. A sufficient condition on practical Mittag Leffler stability is given by using a Lyapunov function. In addition, we study the problem of stability and stabilization for some classes of fractional-order systems.

Vibration Control of an Axially Moving Belt by a Nonlinear Boundary Control

  • Park, Ji-Yun;Hong, Keum-Shik
    • 제어로봇시스템학회:학술대회논문집
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    • 2001.10a
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    • pp.38.1-38
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    • 2001
  • In this paper, the vibration suppression problem of an axially moving power transmission belt is investigated. The equations of motion of the moving belt is first derived by using Hamilton´s principle for systems with changing mass. The total mechanical energy of the belt system is considered as a Lyapunov function candidate. Using the Lyapunov second method, a nonlinear boundary control law that guarantees the uniform asymptotic stability is derived. The control performance with the proposed control law is simulated. It is shown that a boundary control can still achieve the uniform stabilization for belt systems.

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Robust stability of linear system with unstructured uncertainty (비구조적인 불확정성을 갖는 선형시스템의 강인 안정성)

  • 김진훈;변증남
    • 제어로봇시스템학회:학술대회논문집
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    • 1991.10a
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    • pp.52-54
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    • 1991
  • In this paper, the robust stability, and the quadratic performance of linear uncertain systems are studied. A quadratic Lyapunov function candidate with time-varying matrix is derived to provide robust stability bounds. Also upper bounds of a quadratic performance is given under the assumption that the uncertain system is stable. Both the robust stability bounds and the upper bounds of a quadratic performance are obtained as solutions of a class of modified Lyapunov equations.

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Adaptive control of flexible joint robot manipulators (유연성 관절 로봇 매니퓰레이터 적응 제어)

  • 신진호;이주장
    • 제어로봇시스템학회:학술대회논문집
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    • 1992.10a
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    • pp.260-265
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    • 1992
  • This paper presents an adaptive control scheme for flexible joint robot manipulators. This control scheme is based on the Lyapunov direct method with the arm energy-based Lyapunov function. The proposed adaptive control scheme uses only the position and velocity feedback of link and motor shaft. The adaptive control system of flexible joint robots is asymptotically stable regardless of the joint flexibility value. Therefore, the assumption of weak joint ealsticity is not needed. Also, joint flexibility value is unknown. Simulation results are presented to show the feasibility of the proposed adaptive control scheme.

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BOUNDEDNESS RESULTS FOR IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

  • LI HUA;LUO ZHIGUO
    • Journal of applied mathematics & informatics
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    • v.18 no.1_2
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    • pp.261-272
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    • 2005
  • In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

Stability of Time-Varying Discrete State Delay Systems (이산 시변 상태지연시스템의 안정성)

  • Suh, Young-Soo
    • The Transactions of the Korean Institute of Electrical Engineers D
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    • v.51 no.2
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    • pp.43-47
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    • 2002
  • Stability conditions of time-varying discrete state delay systems are proposed. The time-varying state delay is assumed that (i) the magnitude is known to lie in a certain interval (ii) the upper bound of the rate of change is known. Under these conditions, new stability conditions are derived based on switched Lyapunov functions. Stability conditions for both fast time-varying and slowly time-varying delay are considered.

Linear/Nonlinear Sliding Patch and Stuck Phenomena and Applications of Linear/Nonlinear Sliding Patch and Stuck (선형/비선형 슬라이딩 패치 및 스턱현상과 그 응용)

  • Kim, Jin-Wan;Ham, Woon-Chul
    • Journal of Institute of Control, Robotics and Systems
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    • v.6 no.7
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    • pp.523-528
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    • 2000
  • In this short note the characteristics of a nonlinear system of which the state trajectories are oscillating in the phase plane are overviewed. The physical concept of stuck and sliding patch phenomena are also introduced by adding some switching functions and their stability on the sliding patches are analyzed by using the Lyapunov stability theory and Frobenius theorem.

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STABILITY OF A CLASS OF DISCRETE-TIME PATHOGEN INFECTION MODELS WITH LATENTLY INFECTED CELLS

  • ELAIW, A.M.;ALSHAIKH, M.A.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.22 no.4
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    • pp.253-287
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    • 2018
  • This paper studies the global stability of a class of discrete-time pathogen infection models with latently infected cells. The rate of pathogens infect the susceptible cells is taken as bilinear, saturation and general. The continuous-time models are discretized by using nonstandard finite difference scheme. The basic and global properties of the models are established. The global stability analysis of the equilibria is performed using Lyapunov method. The theoretical results are illustrated by numerical simulations.