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A note on persistency of excitation

Record type: Article

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.

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Citation

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.

More information

Published date: 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 262195
URI: http://eprints.soton.ac.uk/id/eprint/262195
PURE UUID: 5c827b45-899f-460a-8c91-c1906268731d

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Date deposited: 29 Mar 2006
Last modified: 18 Jul 2017 08:54

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Contributors

Author: Jan C. Willems
Author: Paolo Rapisarda
Author: Ivan Markovsky
Author: Bart L.M. de Moor

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