New Methods for Estimating the Distance to Uncontrollability

Controllability is a fundamental concept in control theory. Given a linear control system, we present new algorithms for estimating its distance to uncontrollability, i.e., the norm of the norm-wise smallest perturbation that makes the given system uncontrollable. Many algorithms have been previously proposed to estimate this distance. Our new algorithms are the rst that correctly estimate this distance at a cost polynomial in dimension of the given system. We report results from some numerical experiments that demonstrate the reliability and eeectiveness of these new algorithms.