• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.161-166
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• 1997

We obtained sufficient conditions for $\phi$(t)-stability and uniform $\phi$(t)-stability of the trivial solution of comparison differential system. we also investigated the corresponding stability concepts of the trivial solution of the differential system using the thoery of differential inequlities through cones and the method of conevalued Lyapunov functions.

• Structural Engineering and Mechanics
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• v.3 no.4
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• pp.313-324
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• 1995

Flexible cantilever pipes conveying fluids with high velocity are analysed for their dynamic response and stability behaviour. The Young's modulus and mass per unit length of the pipe material have a stochastic distribution. The stochastic fields, that model the fluctuations of Young's modulus and mass density are characterized through their respective means, variances and autocorrelation functions or their equivalent power spectral density functions. The stochastic non self-adjoint partial differential equation is solved for the moments of characteristic values, by treating the point fluctuations to be stochastic perturbations. The second-order statistics of vibration frequencies and mode shapes are obtained. The critical flow velocity is first evaluated using the averaged eigenvalue equation. Through the eigenvalue equation, the statistics of vibration frequencies are transformed to yield critical flow velocity statistics. Expressions for the bounds of eigenvalues are obtained, which in turn yield the corresponding bounds for critical flow velocities.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2006.04a
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• pp.589-596
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• 2006

An improved numerical method to obtain the exact element stiffness matrix is newly proposed to perform the spatially coupled elastic and stability analyses of non-symmetric thin-walled beam-columns with two-types of elastic foundation. This method overcomes drawbacks of the previous method to evaluate the exact stiffness matrix for the spatially coupled stability analysis of thin-walled beam-column. This numerical technique is firstly accomplished via a generalized eigenproblem associated with 14 displacement parameters by transforming equilibrium equations to a set of first order simultaneous ordinary differential equations. Then exact displacement functions are constructed by combining eigensolutions and polynomial solutions corresponding to non-zero and zero eigenvalues, respectively. Consequently an exact stiffness matrix is evaluated by applying the member force-deformation relationships to these displacement functions.

• Nuclear Engineering and Technology
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• v.51 no.1
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• pp.163-169
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• 2019

The robust controller synthesis and analysis of the water level process in the U-tube system generator (UTSG) is addressed in this paper. The parameter uncertainties of the steam generator (SG) are modeled as multiplicative perturbations which are normalized by designing suitable weighting functions. The relative errors of the nominal SG model with respect to the other operating power level models are employed to specify the weighting functions for normalizing the plant uncertainties. Then, a robust controller is designed based on ${\mu}$-synthesis and D-K iteration, and its stability robustness is verified over the whole range of power operations. A gain-scheduled controller with $H_{\infty}$-synthesis is also designed to compare its robustness with the proposed controller. The stability analysis is accomplished and compared with the previous QFT design. The ${\mu}$-analysis of the system shows that the proposed controller has a favorable stability robustness for the whole range of operating power conditions. The proposed controller response is simulated against the power level deviation in start-up and shutdown stages and compared with the other concerning controllers.

• Honam Mathematical Journal
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• v.32 no.4
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• pp.537-544
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• 2010

We prove the superstability of a functional inequality associated with general exponential functions as follows; ${\mid}f(x+y)-a^{x^2y+xy^2}g(x)f(y){\mid}{\leq}H_p(x,y)$. It is a generalization of the superstability theorem for the exponential functional equation proved by Baker.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.61 no.10
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• pp.1508-1512
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• 2012

This paper presents a relaxed stability condition for continuous-time affine fuzzy system using fuzzy Lyapunov function. In the previous studies, stability conditions for the affine fuzzy system based on quadratic Lyapunov function have a conservativeness. The stability condition is considered by using the fuzzy Lyapunov function, which has membership functions in the traditional Lyapunov function. Based on Lyapunov-stability theory, the stability condition for affine fuzzy system is derived and represented to linear matrix inequalities(LMIs). And slack matrix is added to stability condition for the relaxed stability condition. Finally, simulation example is given to illustrate the merits of the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.32 no.2
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• pp.287-296
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• 1995

Wets ([4],[5],[6]) considered single objective linear two-stage programming problem under uncertainty with complete recourse. Artstein, Dupacova, Romisch, Schultz and Wets studied stability of this problem id depth. But in many real world problems to make best decision, we need multiple objective functions. So we consider the following multiple objective two-stage programming problems with complete fixed recourse.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.11-17
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• 1988

For a given autonomous system x' = f(x), we obtain some properties on the location of positive limit sets and investigate some stability concepts which are based upon the existence of Liapunov functions.

• Journal of the Chungcheong Mathematical Society
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• v.3 no.1
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• pp.69-81
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• 1990

In this paper we investigate the problem of exponential asymptotic stability (EAS) in perturbed nonlinear systems of the differential system x' = f(t, x). Also, a simple method for constructing Liapunov functions is used to prove a kind of Massera type converse theorem.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.451-452
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• 2007

In this paper, we simulate power system transient stability using object-oriented programming(OOP). OOP is a more flexible method than procedual programming. There are several advantages in dynamic system simulation using OOP. We also calculate critical fault clearing time using energy functions for detailed models.