Dp 149 en

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Effective computations with polynomial matrices in MATHEMATICA software with applications in control[edit]

Author: Kujan Petr

Diplomové práce 2004

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This diploma thesis deals with the implementation of e�ective algorithms for calculations using polynomial matrices in the framework of the programMATHEMATICA focused on the analysis and design of control systems. Even though MATHEMATICA is a very powerful tool that includes many functions for calculation with scalar polynomials or matrices where individual elements form scalar polynomials, such a direct input of a mathematical problem using standard functions fails - the computing time for large matrices of higher orders is too (extremely) long. Therefore, special algorithms have been developed. In addition, the functions frequently used for design and analysis of control systems are missing in the system (solution of the Diophantine or symmetrical equations, etc.). New functions have been proposed in the system MATHEMATICA with respect to the possibility to use nonnumeric polynomial matrices containing symbols (parameters). The functions that we have implemented were derived from the successful product The Polynomial Toolbox for MATLAB. The work has also been motivated by the fact that the authors of MATHEMATICA system support the design of control systems in their autonomous commercial extension package CONTROL SYSTEM PROFESSIONAL. Some of the functions we created could be well applicable in combination with this tool to signi�cantly reduce the computing time.

Dp 2004 kujan petr.pdf