• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.6A
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• pp.524-532
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• 2002

This paper reports that the Lambert W function applies to a non-iterative design of minimum mean square-error scalar quantizers for a Laplacian source. Specifically, it considers a non-iterative design algorithm for optimum quantizers for a Laplacian source; it finds that the solution of the recursive nonlinear equation in the non-iterative design is elegantly expressed in term of the principal branch of the Lambert W function in a closed form; and it proves that the non-iterative algorithm applies only to exponential or Laplacian sources. The contribution of the paper is in the reduction of the time needed for the design and the increased accuracy in resulting quantization points and thresholds, because the algorithm is non-iterative and the Lambert W function can be evaluated as accurately as desired. Also, numerical results show how optimal quantization distortion converges monotonically to the Panter-Dite constant and help derive an approximation formula for the key parameters of optimum quantizers.

• Proceedings of the IEEK Conference
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• 2001.06a
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• pp.333-336
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• 2001

This paper reports that the Lambert W function applies to a non-iterative design of minimum mean square-error scalar quantizers for a Laplacian source. The contribution of the paper is in the reduction of the time needed for the design and the increased accuracy in resulting quantization points and thresholds, because the algorithm is non-iterative and the Lambert W function can be evaluated as accurately as desired.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.8
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• pp.1144-1150
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• 2013

The stabilizing controller design problem of time-delay singularly perturbed systems is considered. The proposed approach is based on the $H_{\infty}$ norm and the composite control method. A sufficient condition for the stability of the time-delay slow subsystem is presented. Using this condition, we can construct the composite control law for the time-delay singularly perturbed system and analysis the system by the matrix Lambert W function. Illustrated examples are presented to demonstrate the validity and applicability of the proposed method.

• Journal of Power System Engineering
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• v.18 no.1
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• pp.120-127
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• 2014

In this study, Design methods of stabilizing controller for time-delay pure singularly perturbed systems are proposed. Based on the Chang transformation and Lambert W function, we decompose the time-delayed pure singularly perturbed systems into completely decoupled subsystems and derive sufficient stability conditions for $2{\times}2$ time-delayed pure singularly perturbed systems. An illustrated example is presented to demonstrate the validity and applicability of the proposed methods.

• 한국태양에너지학회:학술대회논문집
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• 2011.11a
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• pp.278-281
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• 2011

This system can predict the maximum output about all illumination levels so that the PV system designer can design the system having the best efficiency. For the output prediction exact about the solar cell, that is the device the basis most in the PV system, the basis has to be in order to try this way. The solution based on Lambert W-function are presented to express the transcendental current-voltage characteristic containing parasitic power consuming parameters like series and shunt resistances. A simple and efficient method for the extraction of a single current-voltage (I-V) curve under the constant illumination level is proposed. With the help of the Lambert W function, the explicit analytic expression for I is obtained. And the explicit analytic expression for V is obtained. This analytic expression is directly used to fit the experimental data and extract the device parameters. The I-V curve of the solar cell was expressed through the modeling using Lambert W-function and the numerical formula where there is the difficulty could be logarithmically expressed This method expresses with the I-V curve through the modeling using Lambert W-function which adds other loss ingredients to the equation2 as to the research afterward. And the solar cell goes as small and this I-V curve can predict the power penalty in the system unit.