• Journal of Welding and Joining
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• v.16 no.6
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• pp.86-96
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• 1998

This study proposes the analysis method of time series ultrasonic signal using the chaotic feature extraction for degradation extent evaluation. Features extracted from time series data using the chaotic time series signal analyze quantitatively degradation extent. For this purpose, analysis objective in this study is fractal dimension, lyapunov exponent, strange attractor on hyperspace. The lyapunov exponent is a measure of the rate at which nearby trajectories in phase space diverge. Chaotic trajectories have at least one positive lyapunov exponent. The fractal dimension appears as a metric space such as the phase space trajectory of a dynamical system. In experiment, fractal correlation) dimensions, lyapunov exponents, energy variation showed values of 2.217∼2.411, 0.097∼ 0.146, 1.601∼1.476 voltage according to degardation extent. The proposed chaotic feature extraction in this study can enhances precision ate of degradation extent evaluation from degradation extent results of the degraded materials (SA508 CL.3)

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.4
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• pp.313-318
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• 2002

A robust attitude controller using Lyapunov redesign technique for spacecraft is proposed. In this controller, qua- ternion feedback is considered to have the attitude maneuver capability very close to the eigen-axis rotation. The controller consists of three parts: the nominal feedback parts which is a PD-type controller for the nominal system without uncertainties, the additional term compensating for the gyroscopic motion, and the third part for ensuring robustness to uncertainties. Lyapunov stability criteria is applied to stability analysis. The performance of the proposed controller is demonstrated via computer simulation.

• International Journal of Aeronautical and Space Sciences
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• v.4 no.1
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• pp.99-109
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• 2003

Attitude control law synthesis for the three-axis attitude maneuver of a flexible spacecraft model is presented in this study. The basic idea is motivated by previous works for the extension into a more general case. The new case includes gravitational gradient torque which has significant effect on a wide range of low earth orbit missions. As the first step, the fully nonlinear dynamic equations of motion are derived including gravitational gradient. The control law design based upon the Lyapunov approach is attempted. The Lyapunov function consists of a weighted combination of system kinetic and potential energy. Then, a set of stabilizing control law is derived from the basic Lyapunov stability theory. The new control law is therefore in a general form partially validating the previous work in some sense.

• Proceedings of the KIEE Conference
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• 2003.11b
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• pp.315-318
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• 2003

This paper proposes a switching control method applicable to any affine, 2nd order nonlinear system with single input. The key contribution is to develop a control design method which uses a piecewise continuous Lyapunov function non-increasing at every discontinuous point. The proposed design method requires no restrictions except full state availability. To obtain a non-increasing, piecewise continuous Lyapunov function, we change the sign of off-diagonal term s of the positive definite matrix composing the former Lyapunov function according to the sign of the Inter-connection term. And we use the solution of inequalities which guarantee each Lyapunov function is non-increasing at any discontinuous point.

• KIEE International Transaction on Systems and Control
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• v.2D no.2
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• pp.97-107
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• 2002

In this paper, we propose the concept of orthonormalized compressed measurement for the stability analysis of discrete linear time-varying Kalman filters. Unlike previous studies that deal with the homogeneous portion of Kalman filters, the proposed Lyapunov method directly deals with the stochastically-driven system. The orthonorrmalized compressed measurement provides information on the a priori state estimate of the Kalman filter at the k-th step that is propagated from the a posteriori state estimate at the previous block of time. Since the complex multiple-step propagations of a candidate Lyapunov function with process and measurement noises can be simplified to a one-step Lyapunov propagation by the orthonormalized compressed measurement, a stochastic radius of attraction can be derived that would be impractically difficult to obtain by the conventional multiple-step Lyapunov method.

• Structural Engineering and Mechanics
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• v.52 no.3
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• pp.525-540
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• 2014

The Lyapunov exponent and moment Lyapunov exponents of Hill's equation with frequency and damping coefficient fluctuated by correlated wideband random processes are studied in this paper. The method of stochastic averaging, both the first-order and the second-order, is applied. The averaged $It\hat{o}$ differential equation governing the pth norm is established and the pth moment Lyapunov exponents and Lyapunov exponent are then obtained. This method is applied to the study of the almost-sure and the moment stability of the stationary solution of the thin simply supported beam subjected to time-varying axial compressions and damping which are small intensity correlated stochastic excitations. The validity of the approximate results is checked by the numerical Monte Carlo simulation method for this stochastic system.

• 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.

• Proceedings of the KIEE Conference
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• 2004.05a
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• pp.13-15
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• 2004

In this paper, we propose a novel stability criterion and a guideline of controller design for switched linear systems. Unlike existing criterions such as Lie algebraic method and multiple Lyapunov functions method, the proposed criterion can be applied to each individual system without considering an overall system. By applying the proposed criterion to each individual system separately, a state feedback controller can be easily designed. Stability of the overall system is proved by developing a rule to determine non-increasing Lyapunov functions recursively at each switching instant. An illustrative example is given.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.155-158
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• 1997

In this paper, we present new results concerning the relationship between the input-output and Lyapunov stability of nonlinear system possessing a periodic orbit. Definition of small-signal finite-gain L$\sub$p/ stability around periodic orbit is introduced. We show L$\sub$p/ stability of exponentially stable periodic orbit using quadratic Lyapunov functions for the periodic orbit. The L$\sub$2/ gain analysis is presented with Hamiltonian-Jacobi inequality along with an example.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.457-462
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• 1996

Recently Hurley [3] proved that if A is a weak attractor of a discrete dyanamical system f then there exists a Lyapunov-like function for A. The purpose of this note is to study whether the converse of the above result does hold or not.