• Earthquakes and Structures
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• v.11 no.2
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• pp.297-313
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• 2016

A virtual parameter is introduced into the formulation of the previously published integration method to improve its stability properties. It seems that the numerical properties of this integration method are almost unaffected by this parameter except for the stability property. As a result, it can have second order accuracy, explicit formulation and controllable numerical dissipation in addition to the enhanced stability property. In fact, it can have unconditional stability for the system with the instantaneous degree of nonlinearity less than or equal to the specified value of the virtual parameter for the modes of interest for each time step.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.4
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• pp.788-792
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• 2010

The problem of delay-dependent and parameter-dependent robust stability condition for discrete-time uncertain singular systems with polytopic uncertainty and interval time-varying delay is considered. A new robust stability condition based on parameter-dependent Lyapunov function is derived in terms of LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general condition for both singular and non-singular systems. A numerical example is presented to demonstrate the effectiveness of the proposed method.

• Smart Structures and Systems
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• v.23 no.6
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• pp.641-651
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• 2019

The stochastic stability control of the parameter-excited vibration of an inclined stay cable with multiple modes coupling under random and periodic combined support disturbances is studied by using the direct eigenvalue analysis approach based on the response moment stability, Floquet theorem, Fourier series and matrix eigenvalue analysis. The differential equation with time-varying parameters for the transverse vibration of the inclined cable with control under random and deterministic support disturbances is derived and converted into the randomly and deterministically parameter-excited multi-degree-of-freedom vibration equations. As the stochastic stability of the parameter-excited vibration is mainly determined by the characteristics of perturbation moment, the differential equation with only deterministic parameters for the perturbation second moment is derived based on the $It{\hat{o}}$ stochastic differential rule. The stochastically and deterministically parameter-excited vibration stability is then determined by the deterministic parameter-varying response moment stability. Based on the Floquet theorem, expanding the periodic parameters of the perturbation moment equation and the periodic component of the characteristic perturbation moment expression into the Fourier series yields the eigenvalue equation which determines the perturbation moment behavior. Thus the stochastic stability of the parameter-excited cable vibration under the random and periodic combined support disturbances is determined directly by the matrix eigenvalues. The direct eigenvalue analysis approach is applicable to the stochastic stability of the control cable with multiple modes coupling under various periodic and/or random support disturbances. Numerical results illustrate that the multiple cable modes need to be considered for the stochastic stability of the parameter-excited cable vibration under the random and periodic support disturbances, and the increase of the control damping rather than control stiffness can greatly enhance the stochastic stability of the parameter-excited cable vibration including the frequency width increase of the periodic disturbance and the critical value increase of the random disturbance amplitude.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2000.11a
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• pp.135-142
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• 2000

The adjusting parameter set which enable control systems to locate on stability limit can be derived from theoretical or trial methods for an existing real system. The data from the results are much available to keep a system in the Proper stability condition even to site engineers who are inexperienced in the control system. In this paper, a general one loop control system was adopted for a model system the process of which was assumed to consist of a time-delay element and a first order-lag element in series. After obtaining the corresponding parameter set for the model system by mathematical procedures, their loci on the parameter space was taken according to frequency change. The parameter set loci of stability limit showed unique pattern, and particularity , the curves on the Kg-Ti parameter space were able to be generalized in the form of, an unique exponential formula. These properties were also compared with the results taken from experimental procedures by Nyquist response method and Ziegler & Nichols method on the time domain, and both results were confirmed to be nearly same.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.47 no.4
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• pp.1-6
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• 2010

In this paper, we present a new delay-dependent and parameter-dependent robust stability condition for uncertain singular systems with polytopic parameter uncertainties and time-varying delay. The robust stability criterions based on parameter-dependent Lyapunov function are expressed as LMI (linear matrix inequality). Moreover, the proposed robust stability condition is a general algorithm for both singular systems and non-singular systems. Finally, numerical examples are presented to illustrate the feasibility and less conservativeness of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.14 no.2
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• pp.331-338
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• 1990

In adaptive control, the lack of persistent and rich excitation causes the estimated parameters to drift, which degrade the performance of the system and may introduces instability to the system in a stochastic environment. To solve the problem of the parameter drift, the concept of single parameter adaptation is presented. For the parameter identification, a priori error is directly used for adaptation error. The structure of the controller is based upon the minimum variance control technique. The stability and robustness analysis is carried out by the sector stability theorem for the second order system. The computer simulation is performed to justify the theoretical analysis for the various cases.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.596-601
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• 2000

The paper presents free vibration and stability analyses of a non-uniform Timoshenko beam resting on a two-parameter elastic soil. The soil parameters can vary along the spat and is assumed to be two-parameter model including the effects of both transverse shear deformation and elastic foundation Governing equations related to the vibration and the stability of the beam are derived from Hamilton's principle, and the resulting eigen-value problems can be solved to give natural frequencies and critical force by finite element method. Numerical results for both vibration and stability of beams under an axial force are presented and compared with other available solutions. Finally, vibration frequencies, mode shapes and critical forces are investigated for various thickness ratios, shear foundation parameter, Winkler foundation parameter and boundary conditions of tapered Timoshenko beams.

• Journal of the Korea Society for Simulation
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• v.8 no.2
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• pp.111-122
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• 1999

The paper presents a stability analysis of uniform Timoshenko beams resting on two-parameter elastic foundations. The two-parameter elastic foundations were considered as a shearing layer and Winkler springs in soil models. Governing equations of motion were derived using the Hamilton's principle and finite element analysis was performed and the eigenvalues were obtained for the stability analysis. The numerical results for the buckling stability of beams under axial forces are demonstrated and compared with the exact or available confirmed solutions. Finally, several examples were given for Euler-Bernoulli and Timoshenko beams with various boundary conditions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.11
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• pp.3549-3559
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• 1996

In this study, the effect of parameter and modal filter errors on the vibration control characteristics of flexible structures is analyzed for IMSC ( Independent Modal Space Control). If the control force is designed on the basis of the mathematical model with the parameter and modal filter errors, the closed-loop performance of the vibration control system will be degraded depending on the magnitude of the errors. An asymptotic stability condition of the system with parameter and modal filter errors has more significant effect on the stability condition of the system with parameter and modal filter errors has been drived using Lyapunov approach. It has been found that modal filter error has more significant effect on the stability of closed-loop system than parameter error does. The extent of the response deviation of the closed-loop system is also derived and evaluated using operator thchniques.

• 제어로봇시스템학회:학술대회논문집
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• 1995.10a
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• pp.5-9
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• 1995

In many cases of robust stability problems, the characteristic polynomial has real coefficients which or nonlinear functions of uncertain parameters. For this set of polynomials, a new stability easily checking algorithm for reducing the conservatism of the stability bound are given. It is the new stability theorem to determine the stability region just in parameter space. Illustrative example show that the presented method has larger stability bound in uncertain parameter space than others.