Canonical form under strong equivalence transformations and controllability indexes in singular systems

The singular controller canonical form for singular systems is presented. Such a canonical form appears to extend both the well-known controller canonical form and the generalized controller canonical form, which was developed recently. It is shown that any singular system is strongly equivalent to such a canonical form if and only if it is controllable. Another result of this study is to establish a connection between the minimal indexes of a certain matrix pencil and the controllability indexes defined using the canonical form.<>