• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1133-1143
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• 2009

In this work, we successfully extended dimensional differential transform method (DTM), by presenting and proving some new theorems, to solve the non-linear matrix differential Riccati equations(first and second kind of Riccati matrix differential equations). This technique provides a sequence of matrix functions which converges to the exact solution of the problem. Examples show that the method is effective.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1453-1467
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• 2007

By means of a Riccati transform some oscillation or nonoscillation criteria are established for nonlinear differential equations of second order $$(E_1)\;[p(t)|x#(t)|^{\alpha}sgn\;x#(t)]#+q(t)|x(\tau(t)|^{\alpha}sgn\;x(\tau(t))=0$$. $$(E_2),\;(E_3)\;and\;(E_4)\;where\;0<{\alpha}$$ and $${\tau}(t){\leq}t,\;{\tau}#(t)>0,\;{\tau}(t){\rightarrow}{\infty}\;as\;t{\rightarrow}{\infty}$$. In this paper we improve some previous results.

• Bulletin of the Korean Mathematical Society
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• v.45 no.2
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• pp.241-252
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• 2008

By means of a Riccati transform and averaging technique some oscillation criteria are established for perturbed nonlinear differential equations of second order $(P_1)\;(p(t)x'(t))'+q(t)|x({\phi}(t)|^{{\alpha}+1}sgnx({\phi}(t))+g(t,\;x(t))=0$ $(P_2)$ and $(P_3)$ satisfying the condition (H). A comparison theorem and examples are given.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.9
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• pp.36-42
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• 1997

Optical filters with graded index profiles are designed by applying the fourier transform to a riccati equation which governs the reflection and transmission characteristics of inhomogeneous refractive index distributions. The inhomogeneous refractive index profile of an optical filter with specified target spectrum is obtained through iterations. The spectra response of the inhomogeneous refractive index layers are analyzed by using runge-dutta numerical method to solve the differential euations of the amplitude and the phase of reflection coefficient derived from the riccati equation and the results are in good agreement with the resutls obtained by using matrix method.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.37 no.3
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• pp.28-34
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• 2000

In this paper, we derive a spectral function and a new impedance profile of non-uniform tapered transmission lines by applying the Fourier transform to a linearized Riccati equation. We compensate the error which is from a linearized Riccati equation by adding a Taylor series to the impedance profile. Added terms remove discontinuities In the impedance profile at both ends of the non-uniform section. We show that a calculated spectrum approaches to a target spectrum of filter by an iterative method and numerical examples are given to illustrate the role of the phase function. As the design method which is shown in present paper provides a excellent adaptability for the design of non-uniform tapered transmission lines, the present method can be applied to design filters and impedance matching circuits with various passband characteristics.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.10 no.2
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• pp.291-301
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• 1999

A method for the synthesis of one-dimensional nonlinear distribution function is presented for the desired inverse scattering pattern. This method is based on the inverse transform of the solution of the Riccati equation derived from one-dimensional inverse scattering problem. Since the solution is analogous to the array factor or normalized space factor in collinear array antenna, the synthesis method for field pattern is applied for the construction of the involved line-source nonlinear distribution function. The suggested method is carried out under the optimization process, and is numerically verified by synthesizing the dispersive transmission line profile within the specified frequency band and control of scattered field on resistive strip.

• Journal of Institute of Control, Robotics and Systems
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• v.4 no.2
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• pp.157-162
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• 1998

This paper provides some properties of positive real systems in time domain. It is well-known that a positive real system and a bounded real system are closely related by bilinear transform in a frequency domain. By using supply rate and storage function, we show that a positive real system can be transformed into a bounded real system, and that a positive real system can be transformed into another positive real system with in a time domain. Also, we show that an ESPR(extended strictly positive real) system can be decomposed into a feedback system of lossless positive real system and another ESPR system. These results may be used to design an output feedback controller for mixed H$H_2$ESPR problem.