A Persistency of Excitation Condition for Continuous-Time Systems

We study identifiability for linear, continuous time-invariant systems. We state sufficient conditions on an input trajectory
$\widehat {u}$
and a finite number of its derivatives, in order to be able to deduce all differential equations describing the data-generating system from any corresponding input-output sequence
$(\widehat {u},\widehat {y})$
on a finite interval.