Singular pencils arise naturally in the study of linear
control systems
,
.
Here
is a control input that the user attempts
to select to make sure the state variable
and output variable
attain desired values.
Concepts such as controllability, controllable subspace,
controllable and uncontrollable modes,
observability, etc. can all be formulated and computed
in terms of reducing subspaces and eigenvalues
[460,447,451,450].