Detectability

The following are equivalent:

• (*C,A*) is
detectable.

•* A+LC * is stable for a
suitable L.

• (*A*****,C**) is
controllable.

• The matrix has full column rank for all *Re**l*³* 0.*

•** **For all *l* and *y* such that *Ay= **l**y*, *Re**l** *³*0, *and *Cy**¹** 0.*