Estimating distances from quadruples satisfying stability properties to quadruples not satisfying them (Q5946200)

The paper deals with the quadruples of matrices \((E,A,B,C)\) defining generalized linear multivariable time-invariant dynamical systems given by the equations \(E \dot{x}(t)=Ax(t)+Bu(t)\) and \(y(t)=Cx(t)\), where \(A\) and \(E\) are square matrices of order \(n\) and \(B\) and \(C\) have sizes \(n \times m\) and \(p \times n\), respectively.NEWLINENEWLINEThe authors obtain, using geometrical techniques, lower bounds for the Frobenius distance between structurally stable quadruples \((E,A,B,C)\) and non-structurally stables ones. They also obtain upper bounds for the distance from the contrallable and observable quadruple \((I_n,A,B,C)\) to the nearest uncontrollable and unobservable quadruple measured with this distance.