• 제어로봇시스템학회:학술대회논문집
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• 1999.10a
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• pp.112-115
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• 1999

A new method to solve a Lyapunov equation for a discrete delay system is proposed. Using this method, a Lyapunov equation can be solved from a simple linear equation and N-th power of a constant matrix, where N is the state delay. Combining a Lyapunov equation and frequency domain stability, a new stability condition is proposed. The proposed stability condition ensures stability of a discrete state delay system whose state delay is not exactly known but only known to lie in a certain interval.

• Journal of Institute of Control, Robotics and Systems
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• v.1 no.2
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• pp.78-82
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• 1995

In this paper, we consider the robustness analysis problem in state space models with linear time invariant perturbations. Based upon the discrete-time Lyapunov approach, sufficient conditions are derived for the eigenvalues of perturbed matrix to be located in a circle, and robustness bounds on perturbations are obtained. Spaecially, for the case of a diagonalizable hermitian matrix the bound is given in terms of the nominal matrix without the solution of Lyapunov equation. This robustness analysis takes account not only of stability robustness but also of certain types of performance robustness. For two perturbation classes resulting bounds are shown to be improved over the existing ones. Examples given include comparison of the proposed analysis method with existing one.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.936-941
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• 1987

This paper prexents an adaptive control scheme which adjusts any deviations of the manipulator from a desired trajectory. The scheme combines a new adaptive control and the conventional nominal control which drives the manipulator to the neighborhood of the trajectory. The proposed adaptive control is developed based on the lineatized perturbation equations in the vicinity of the trajectory and the Lyapunov design method, which makes the perturbations exponentially decay and has less computational requirements than the existing ones.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.10
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• pp.1894-1899
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• 2010

This note is concerned with a robust sliding mode control(SMC) for a class of unmatched uncertain system with severe commensurate state time delay. The suggested method is extended to the control of severe state time delay systems with unmatched uncertainties except the matched input matrix uncertainty. A transformed sliding surface is proposed and a stabilizing control input is suggested. The closed loop stability together with the existence condition of the sliding mode on the proposed sliding surface is investigated through one Lemma and two Theorems by using the Lyapunov direct method with the concept of the control Lyapunov function instead of complex Lyapunov-Kravoskii functionals. Through an illustrative example and simulation study, the usefulness of the main results is verified.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.251-266
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• 2004

We consider a controlled nonlinear mechanical system described by the Lagrange equations. We determine the control forces $Q_1$ and the restrictions for the perturbations $Q_2$ acting on the mechanical system which allow to guarantee the asymptotic stability of the program motion of the system. We solve the problem of stabilization by the direct Lyapunov's method and the method of limiting functions and systems. In this case we can use the Lyapunov's functions having nonpositive derivatives. The following examples are considered: stabilization of program motions of mathematical pendulum with moving point of suspension and stabilization of program motions of rigid body with fixed point.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.12
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• pp.1615-1623
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• 1997

Numerical study on the chaotic stirring of the screw extruder model proposed has been performed. The velocity field was used in obtaining the trajectories of passive particles for studying the stirring effect of the screw extruder. Two nonlinear dynamical tools, that are Poincare sections and Lyapunov exponents, were used in analysing the stirring effect. The Poincare sections and the Lyapunov exponents show that the stirring effect is most satisfactory, when n(the number of flights in a section) is 1, for the case a (aspect ratio ; flight height divided by the spacing between flights) being O.1. It is also required to set n=3, or 5 at a= 0.2, 0.3 for a uniform stirring.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.7 s.178
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• pp.1689-1696
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• 2000

This paper proposes a new adaptive control scheme for flexible-link robots. A model-based nonlinear control scheme is designed based on a V-shape Lyapunov function, and then the nonlinear control i s extended to a model-based adaptive control to cope with parametric uncertainties in the dynamic model. The proposed control guarantees the global exponential or global asymptotic stability of the overall control system with all internal signals bounded. The effectiveness of the proposed control is shown by computer simulation.

• Journal of Astronomy and Space Sciences
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• v.14 no.2
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• pp.367-374
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• 1997

Slewing maneuver and vibration suppression control of flexible spacecraft model by Lyapunov stability theory are considered. The specific model considered in this paper consists of a rigid hub with an elastic appendage attached to the central hub and tip mass. Attitude control to point and stabilize single axis using reaction wheel type device is tested. To control all flexible modes is so critical to designing an active control law. We therefore considered an direct output feeback control design by using Lyapunov stability theory. It is shown that the ouput feedback control law design with proposed configuration gives satisfactory result in slewing performance and vibration suppression control.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2003.11a
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• pp.47-55
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• 2003

This paper Presents active control algorithm using probability density function of structural energy. It is assumed that the structural energy under excitation has Rayleigh probability distribution. This assumption is based on the fact that Rayleigh distribution satisfies the condition that the structural energy is always positive and the occurrence probability of minimum energy is zero. The magnitude of control force is determined by the probability that the structural energy exceeds the specified target critical energy, and the sign of control force is determined by Lyapunov controller design method. Proposed control algorithm shows much reduction of peak responses under seismic excitation compared to LQR controller, and it can consider control force limit in the controller design. Also, chattering problem which sometimes occurs in Lyapunov controller can be avoided.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.2
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• pp.380-388
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• 1994

Study on the chaotic stirring has been performed numerically and experimentally for a shallow rectangular tank accompanying a vortex shedding. The model is composed of a rectangular tank with a vertical plate with a length half the width of the tank. The tank is subject to a horizontal sinusoidal oscillation. The chaotic stirring was analysed by Poincare sections, unstable manifolds and Lyapunov exponents. As Reynolds number is increased the stirring effect is decreased due to the growth of a regular regions near the lower surface of the tank. In the other hand decrease of Reynolds number gives a weaker vortex shedding resulting in the poorer stirring effect. It was also found that the Lyapunov exponent is the highest at the dimensionless period of 1.3-1.5, which seems to be the best condition for the efficient stirring. The experimental visualization for the deformation of materials exhibits the striation pattern similar to the unstable manifold obtained numerically.