On the identification of state-derivative-coupled systems

This short paper treats one aspect of the identification of state-derivative-coupled systems, such as
M\dot{x}(t) = Ax(t) + Bu(t) + w(t)
where
M \neq I
, and
M
is invertible. This equation can also be written as
\dot{x}(t) = F_{1}x(t) + F_{2}u(t) + \omega(t)
. We assume that reduced form parameters (
F_{1}, F_{2}
) are identifiable and develop a sequence of tests for establishing the identifiability of structural parameters (
M, A, B
) from (
F_{1} F_{2}
). The tests are constructive, in that they not only can be used to ascertain the identifiability of (
M, A, B
); but, if (
M, A, B
) are not identifiable, can also indicate corrective actions to be taken so that (
M, A, B
) are identifiable.