A Persistency of Excitation Condition for Continuous-Time Systems
Paolo Rapisarda, M. Kanat Camlibel, Henk J. van Waarde
Abstract
We study identifiability for linear, continuous time-invariant systems. We state sufficient conditions on an input trajectory <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\widehat {u}$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$(\widehat {u},\widehat {y})$ </tex-math></inline-formula> on a finite interval.