Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them

摘要

We consider quadruples of matrices (E,A,B,C) defining generalized linear\udmultivariable time-invariant dynamical systems, with E,A square matrices\udand B, C rectangular matrices.\udUsing geometrical techniques we present upper bounds and lower bounds for\udthe distances between a quadruple and the nearest structurally unstable,\uduncontrollable and/or unobservable one, in terms of the singular values of\udmatrices associated to the quadruple.