POLMAT: MUPAD LIBRARY FOR POLYNOMIAL MATRICES
AUGUSTA, P.; HURĮK, Z.
Abstract
Polynomial methods, launched in 1970's from Czechoslovakia, are well established approach to linear systems. Ratios of two univariate polynomials are commonly used for description of linear dynamical systems with single input and single output (SISO). Left or right fractions of polynomial matrices generalise in a straightforward way the concept of transfer functions for systems with multiple inputs and multiple outputs (MIMO). The procedures for analysis of properties of dynamical systems and controller design are based on manipulation with algebraic expressions. While the state-space methods, which operate with constant matrices, are included in many software libraries, there are a few packages that can handle polynomial matrices. This paper presents a new freely available library for symbolic computation with polynomial matrices named Polmat. The library is developed for MuPAD, which is an easily accessible efficient computer algebra system and programming language. Polmat comes with a series of new implemented functions, including solvers for linear equations with polynomial matrices and spectral factorisation, and makes possible using MuPAD in control theory and controller design. The focus of MuPAD on symbolic computation was also appreciated because most of the available tools for polynomial matrices rely on numerical algorithms and therefore suffer from the common problems related to rounding. Symbolic algorithms, on the other hand, express real numbers as ratios of two integers, and therefore no errors are introduced into the computation. The price is, however, extreme computational burden. Even with this lowered computational efficiency, symbolic computation can be regarded as a helper with the development of numerical algorithms. Not to mention the educational role. MuPAD with Polmat provides a useful alternative to the few existing numerical libraries for polynomial matrices, accessible to everyone.
Coresponding author e-mail: augusp1[at]control[dot]felk[dot]cvut[dot]cz
Session: Algorithms and Computing for Control
