A note on persistency of excitation

Willems, Jan C., Rapisarda, Paolo, Markovsky, Ivan and de Moor, Bart L.M. (2005) A note on persistency of excitation Systems and Control Letters, 54, pp. 325-329.


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We prove that if a component of the response signal of a controllable linear time-invariant system is persistently exciting of sufficiently high order, then the windows of the signal span the full system behavior. This is then applied to obtain conditions under which the state trajectory of a state representation spans the whole state space. The related question of when the matrix formed from a state sequence has linearly independent rows from the matrix formed from an input sequence and a finite number of its shifts is of central importance in subspace system identification.

Item Type: Article
Organisations: Southampton Wireless Group
ePrint ID: 262195
Date :
Date Event
Date Deposited: 29 Mar 2006
Last Modified: 17 Apr 2017 21:45
Further Information:Google Scholar
URI: http://eprints.soton.ac.uk/id/eprint/262195

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