H2 model reduction using an algebraic approach

This paper proposes a solution approach to the H₂ model reduction problem based on an algebraic method called Gröbner bases. In the proposed approach, a necessary optimality condition is reduced to a set of algebraic equations in terms of the coefficients of the characteristic polynomial of the approximant and an axillary polynomial. Then, all the solutions yielding candidate approximants are computed by means of Gröbner bases, and the optimal approximant which is a real stable system minimizing the H₂ error is chosen from all the candidates. Numerical examples are given to demonstrate the suggested approach.