An algorithm for computing a generalized problem of controllability radii

Given a linear control system, the controllability radii for a linear control system is the norm of the smallest perturbation that makes the given system uncontrollable. In this paper, we propose a generalized problem for controllability radii when both or only one of system matrices is perturbed. Then, based on recent methods of Gu, Burke-Lewis-Overton and Gu-Mengi-Overton-Xia-Zhu, we present an algorithm to computing the generalized controllability radius problem. This algorithm achieves the complexity of O(k⁴) on average, where k is the order of the system. Numerical experiments indicate that the new method is reliable in practice.