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

We consider quadruples of matrices (E,A,B,C) defining generalized linear multivariable time-invariant dynamical systems , y(t)=Cx(t) with A,E square matrices and B,C rectangular matrices. Using geometrical techniques we present upper bounds and lower bounds for the distances between a quadruple and the nearest non-structurally stable, uncontrollable and/or unobservable one, in terms of the singular values of matrices associated to the quadruple.