• Journal of the Chungcheong Mathematical Society
• /
• v.3 no.1
• /
• pp.83-88
• /
• 1990

It is well-known that under suitable conditions, uniform asymptotic stability implies total stability. We prove this theorem of Malkin by using Liapunov-like functions and so our proof is a detailed version of Yoshizawa's proof.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.561-568
• /
• 2011

We investigate the stability property and existence of almost periodic solutions of discrete Volterra equations with unbounded delay.

• 제어로봇시스템학회:학술대회논문집
• /
• 1995.10a
• /
• pp.271-274
• /
• 1995

This paper is concerned with the problem of robust stabilization of uncertain single-input and single-output nonlinear systems. Based on the input/output linearization approach for nonlinear state feedback synthesis in conjunction with Lyapunov methods, a stabilizing state feedback controller is proposed. Compared with the controllers reported in the control literature, instead of uniform ultimate boudedness, the controller proposed in this paper can guarantee uniform asymptotic stability of nonlinear systems in the presence of uncertainties. The required information about uncertain dynamics in the system is only that the uncertainties are bounded in Euclidean norm by known functions of the system state.

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• 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
• /
• 1995.10a
• /
• pp.227-230
• /
• 1995

Stability of a coupled nonautonomous ordinary differential equation is investigated. Asymptotic convergence to zero of a part of state vector is additionally shown, otherwise only uniform stability could have been concluded by the Lyapunov direct method. Obtained results could be particularly useful in analysis of nonautonomous systems in which the invariance principle does not hold. An illustrating example is given.

• 제어로봇시스템학회:학술대회논문집
• /
• 1997.10a
• /
• pp.139-142
• /
• 1997

In this paper, a robust controller is proposed to achieve an accurate tracking for an uncertain nonlinear plant with actuator dynamics. The extent of parameter uncertainty can be quantified by using linear parameterization technique. A switching controller is proposed to guarantee the global asymptotic stability of the plant. In order to eliminate the chattering caused by the switching controller, a smoothing controller is designed using the boundary layer technique around the sliding surface and guarantees the uniform ultimate boundedness of the tracking error.

• 제어로봇시스템학회:학술대회논문집
• /
• 1987.10b
• /
• pp.115-119
• /
• 1987

In this paper the observer design problem in bilinear systems is studied using the Walsh functions as approximating set of functions to find a finite series expansion of the state of bilinear system. A classical Liapnove method, to finding a class of observer feedback matrix, is applied to ensure uniform asymptotic stability of the observation error dynamics. An algorithm is derived for observer state eq. via Walsh function. The basic objective is to develop a computational algorithm for the determination of the coefficients in the expansion. This approach technique gives satisfactory result as well provides precise and effective method for the bilinear observer design problem.

• Journal of Ocean Engineering and Technology
• /
• v.19 no.5 s.66
• /
• pp.58-64
• /
• 2005

In this paper, a feedback linearizing anti-sway control law, using a 2-D model for container cranes, is investigated. The equations of motion are first derived from Lagrange's equation. Then, by substituting the sway dynamics into the trolley dynamics, a reduction of variables from three (trolley, hoist, sway) to two (trolley, hoist) is pursued. The anti-sway control law is designed based on the Lyapunov stability theorem. The proposed control law guarantees the uniform asymptotic stability of the closed-loop system. The simulation results of the derived control law, using MATLAB/Simulink, are compared with those of the sliding mode control law, noted in previous literature. Also, experimental results using a 3-D pilot crane are provided.

• Journal of Institute of Control, Robotics and Systems
• /
• v.19 no.9
• /
• pp.822-826
• /
• 2013

In this paper, we propose an AFDO (Adaptive Fault Diagnosis Observer) and a fault tolerant controller for a class of nonlinear continuous-time system under the nonlinear abrupt actuator faults. Together with its estimation laws, the AFDO which estimates that the actuator faults is designed by using the Lyapunov analysis. Then, based on the designed AFDO, an adaptive sliding mode controller is proposed as the fault tolerant controller. Using Lyapunov stability analysis, we also prove the uniform boundedness of the state, the output and the fault estimation errors, and the asymptotic stability of the tracking error under the nonlinear time-varying faults. Finally, we illustrate the effectiveness of the proposed diagnosis method and the control scheme thorough computer simulations.

• International Journal of Control, Automation, and Systems
• /
• v.5 no.4
• /
• pp.379-387
• /
• 2007

In this paper, a nonlinear anti-sway controller for container cranes with load hoisting is investigated. The considered container crane involves a planar motion in conjunction with a hoisting motion. The control inputs are two (trolley and hoisting forces), whereas the variables to be controlled are three (trolley position, hoisting rope length, and sway angle). A novel feedback linearization control law provides a simultaneous trolley-position regulation, sway suppression, and load hoisting control. The performance of the closed loop system is shown to be satisfactory in the presence of disturbances at the payload and rope length variations. The advantage of the proposed control law lies in the full incorporation of the nonlinear dynamics by partial feedback linearization. The uniform asymptotic stability of the closed-loop system is assured irrespective of variations of the rope length. Simulation and experimental results are compared and discussed.