• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2003년도 ICCAS
• /
• pp.449-451
• /
• 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.

• 한국정밀공학회지
• /
• 제14권4호
• /
• pp.88-96
• /
• 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.

• 대한수학회보
• /
• 제54권4호
• /
• pp.1309-1321
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 2001년도 ICCAS
• /
• pp.38.1-38
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1991년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 22-24 Oct. 1991
• /
• pp.52-54
• /
• 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.

• 제어로봇시스템학회:학술대회논문집
• /
• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국내학술편); KOEX, Seoul; 19-21 Oct. 1992
• /
• pp.260-265
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제18권1_2호
• /
• pp.261-272
• /
• 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.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제51권2호
• /
• pp.43-47
• /
• 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.

• 제어로봇시스템학회논문지
• /
• 제6권7호
• /
• pp.523-528
• /
• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제22권4호
• /
• pp.253-287
• /
• 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.