Constructive Algebra Methods for the L2-Problem For Stable Linear Systems

Abstract

We investigate the feasibility of using computer algebra for solving L2 system approximation problems. The first-order optimally conditions yield a set of polynomial equations which can, in principle, be solved using Groebner basis methods. A general solution along these lines would be tremendously useful, although it does not appear to be feasible at present except for rather low McMillan degrees. We demonstrate that it can be feasible for specific examples; in such cases global optima can be found reliably. We show that the use of a Schwarz-like canonical form simplifies the structure of the problem, and the required computations.