Bounding the Distance from a Controllable Two Order System to a Non-Controllable Ones
Isabel Garc ́ õa-Planas · 2008
We consider quadruples of matrices (E,A1,A2,B) defining two order generalized linear time-invariant dynamical systems E¨ = A1 ˙ x+A2x+ Bu, with E,A1,A2 square matrices and B rectangular matrix. We present upper bounds for the distances between a controllable systems and the nearest non-controllable one, in terms of the singular values of a certain matrix that we will call controllability matrix, associated to the system.