Output details

Approximate zero polynomials of polynomial matrices and linear systems

The new concept of optimal approximate zero polynomial of a polynomial matrix is introduced using the approximate GCD of a set of polynomials and Plucker embedding. For the first time the means for computing the distance from non-coprimeness of a polynomial matrix is given; the computations are expressed as a distance problem in a projective space. We introduce the approximate zero, decoupling zero polynomials of linear systems and their optimal versions. We introduce the orbital distance of state space descriptions (state feedback/output injection) from uncontrollability (unobservability), define feedback invariant distances and the invariant versions of “approximate decoupling polynomials”.