| Abstract: | For a linear control system (A,B), the distance to uncontrollability is characterized by , where σn([A − λI,B]) is the smallest singular value of the augmented matrix [A − λI,B]. Two methods are developed to estimate the distance to uncontrollability, giving both a lower bound and an upper bound. One method is fast, requiring only one spectral decomposition of A and computations of three smallest singular values and being used for well-conditioned A. The other is slow, requiring computations of a large number of the smallest singular values, but it produces bounds as tight as possible and also a region containing global minimizers. Newton's method can be used to compute the global minimizers if one really wants. |
