Filters connecting isospectral quadratic systems

This paper concerns n×n matrix polynomials of the form L(λ)=Mλ2+Dλ+K. We study isospectral pairs L(λ), and show how to construct linear matrix functions (called filters) for which . The ultimate objective is to design filters in such a way that is diagonal – where this is possible. The main result of this paper is a constructive theorem demonstrating that two systems are isospectral if and only if there exists an associated family of coprime filters. Well-established techniques are used in the construction of filters using “standard pairs” for matrix polynomials and “structure preserving transformations” for their linearizations. In this paper, attention is confined to systems with nonsingular leading coefficient, M.