Fast Methods for Estimating the Distance to Uncontrollability

Abstract

The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke-Lewis-Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4 ) operations on average, which is an improvement over previous methods which have complexity O(n6 ), where n is the order of the system. Numerical experiments indicate that the new method is reliable in practice.