scholarly journals ON CONDITIONING FOR A GENERAL SYSTEM OF FOUR POINT BOUNDARY VALUE PROBLEMS

1996 ◽  
Vol 27 (3) ◽  
pp. 219-225
Author(s):  
M. S. N. MURTY
Keyword(s):  
Differential Equation ◽  
Fundamental Matrix ◽  
Close Relationships ◽  
General System ◽  
Point Boundary ◽  
Matrix Differential Equation ◽  
Growth Behaviour ◽  
First Order ◽  
Matrix Differential ◽  
The Stability

In this paper we investigate the close relationships between the stability constants and the growth behaviour of the fundamental matrix to the general FPBVP'S associated with the general first order matrix differential equation.

scholarly journals Stability Analysis of Linear Sylvester System of First Order Differential Equations

2020 ◽  
Vol 9 (11) ◽  
pp. 25252-25259
Author(s):  
Kasi Viswanadh V. Kanuri ◽  
SriRam Bhagavathula ◽  
K.N. Murty
Keyword(s):  
Differential Equation ◽  
Stability Analysis ◽  
Differential Equations ◽  
Stability Criteria ◽  
Matrix Differential Equation ◽  
Bounded Solutions ◽  
First Order ◽  
Matrix Differential ◽  
First Order Differential Equations

    In this paper, we establish stability criteria of the linear Sylvester system of matrix differential equation using the new concept of bounded solutions and deduce the existence of -bounded solutions as a particular case.

scholarly journals Modal waves in multiconductor transmission lines by using fundamental matrix response

2020 ◽  
Vol 42 ◽  
pp. e38
Author(s):  
Julio Cesar Ruiz Claeyssen ◽  
Daniela De Rosso Tolfo ◽  
Rosemaira Dalcin Copetti
Keyword(s):  
Differential Equation ◽  
Transmission Line ◽  
Transmission Lines ◽  
Fundamental Matrix ◽  
Propagation Constant ◽  
Matrix Differential Equation ◽  
Reflection And Transmission ◽  
Admittance Matrix ◽  
Multiconductor Transmission Line ◽  
Matrix Differential

The differential equations that model voltage and current for a multiconductor transmission line are written in matrix form. Supposing a time exponential solution through of the modal analysis the modal waves are obtained and solution of a ordinary matrix differential equation, thus determining the amplitude for voltage and current. The modal waves are given in terms of the fundamental matrix solution associated to the ordinary matrix differential equation. The decomposition of the modal waves in forward and backward propagators are used for determine the reflection and transmission matrices for junction in transmission lines. Circulant symmetric transmission lines are discussed, case in that the values for the self-impedance are the same as well as the mutual-impedance values and the same considerations to the admittance matrix. In particular, for these transmission lines are characterized the propagation constants and is observed that the number of multiconductors has effects only on a specific propagation constant. Numerical example of one multiconductor transmission line is presented allowing to observe important aspects of the methodology developed.

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