Physical Sciences and Mathematics Commons^™

Singularly Perturbed Control Systems Using Non-Commutative Computer Algebra, J. W. Helton, F. Dell Kronewitter, W. M. Mceneaney, Mark Stankus

Mathematics

Most algebraic calculations which one sees in linear systems theory, for example in IEEE TAC, involve block matrices and so are highly non-commutative. Thus conventional commutative computer algebra packages, as in Mathematica and Maple, do not address them. Here we investigate the usefulness of non-commutative computer algebra in a particular area of control theory − singularly perturbed dynamic systems − where working with the non-commutative polynomials involved is especially tedious. Our 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' …