Singularly perturbed control systems using non-commutative computer algebra (Q2704383)

It is well known that most algebraic calculations which one sees in linear systems theory, involve block matrices and so are highly noncommutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. This paper investigates the usefulness of noncommutative computer algebra in a particular area of control theory -- singularly perturbed dynamic systems -- where working with the noncommutative polynomials involved is especially tedious. The conclusion is that they have considerable potential for helping practitioners with such computations. Commutative Gröbner basis algorithms are powerful and make up the engines in symbolic algebra packages' solve commands. Noncommutative Gröbner basis algorithms are more recent, but it is seen that they, together with an algorithm for removing ``redundant equations'', are useful in manipulating the messy sets of noncommutative polynomial equations which arise in singular perturbation calculations. The noncommutative algebra package NCAlgebra and the noncommutative Gröbner basis package NCGB which runs under it on two different problems are used. An example is given to illustrate the usefulness of the proposed methods.