Error Analysis of the Complex Kronecker Canonical Form

In some interesting applications in control and system theory, i.e. in engineering, in ecology (Leslie population model), in financial/actuarial (Leontief multi input - multi output) science, linear descriptor (singular) differential/difference equations with time-invariant coefficients and (non-) consistent initial conditions have been extensively used. The solution properties of those systems are based on the Kronecker canonical form, which is an important component of the Matrix Pencil Theory. In this paper, we present some preliminary results for the error analysis of the complex Kronecker canonical form based on the Euclidean norm. Finally, under some weak assumptions an interesting new necessary condition is also derived.