Rational Implementation Based on the Bilinear Transformation

2006 ◽  
pp. 207-216
Keyword(s):  
Bilinear Transformation

Bilinear Transformation of Polarization

1972 ◽  
Vol 62 (10) ◽  
pp. 1239 ◽  
Author(s):  
L. J. Kaplan
Keyword(s):  
Bilinear Transformation

N-soliton solutions and localized wave interaction solutions of a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyamaf equation

2021 ◽  
pp. 2150277
Author(s):  
Hongcai Ma ◽  
Qiaoxin Cheng ◽  
Aiping Deng
Keyword(s):  
Dynamic Behavior ◽  
Soliton Solution ◽  
Soliton Solutions ◽  
Wave Interaction ◽  
Bilinear Transformation ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Ytsf Equation ◽  
Line Soliton

[Formula: see text]-soliton solutions are derived for a (3 + 1)-dimensional potential-Yu–Toda–Sasa–Fukuyama (YTSF) equation by using bilinear transformation. Some local waves such as period soliton, line soliton, lump soliton and their interaction are constructed by selecting specific parameters on the multi-soliton solutions. By selecting special constraints on the two soliton solutions, period and lump soliton solution can be obtained; three solitons can reduce to the interaction solution between period soliton and line soliton or lump soliton and line soliton under special parameters; the interaction solution among period soliton and two line solitons, or the interaction solution for two period solitons or two lump solitons via taking specific constraints from four soliton solutions. Finally, some images of the results are drawn, and their dynamic behavior is analyzed.

scholarly journals Newmark-FDTD Formulation for Modified Lorentz Dispersive Medium and Its Equivalence to Auxiliary Differential Equation-FDTD with Bilinear Transformation

2019 ◽  
Vol 2019 ◽  
pp. 1-7
Author(s):  
Hongjin Choi ◽  
Jeahoon Cho ◽  
Yong Bae Park ◽  
Kyung-Young Jung
Keyword(s):  
Differential Equation ◽  
Numerical Stability ◽  
Dispersive Medium ◽  
Fdtd Method ◽  
Dispersive Media ◽  
Complex Conjugate ◽  
Dispersion Models ◽  
Bilinear Transformation ◽  
Quadratic Complex ◽  
Difference Time

The finite-difference time-domain (FDTD) method has been popularly utilized to analyze the electromagnetic (EM) wave propagation in dispersive media. Various dispersion models were introduced to consider the frequency-dependent permittivity, including Debye, Drude, Lorentz, quadratic complex rational function, complex-conjugate pole-residue, and critical point models. The Newmark-FDTD method was recently proposed for the EM analysis of dispersive media and it was shown that the proposed Newmark-FDTD method can give higher stability and better accuracy compared to the conventional auxiliary differential equation- (ADE-) FDTD method. In this work, we extend the Newmark-FDTD method to modified Lorentz medium, which can simply unify aforementioned dispersion models. Moreover, it is found that the ADE-FDTD formulation based on the bilinear transformation is exactly the same as the Newmark-FDTD formulation which can have higher stability and better accuracy compared to the conventional ADE-FDTD. Numerical stability, numerical permittivity, and numerical examples are employed to validate our work.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

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