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A note on persistency of excitation

A note on persistency of excitation
A note on persistency of excitation
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.
325-329
Willems, Jan C.
3a5841a4-3cdb-4d99-8cb8-dd02ca641e87
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
de Moor, Bart L.M.
6aba7d23-1605-4d40-b3bd-a5374c813f44
Willems, Jan C.
3a5841a4-3cdb-4d99-8cb8-dd02ca641e87
Rapisarda, Paolo
79efc3b0-a7c6-4ca7-a7f8-de5770a4281b
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
de Moor, Bart L.M.
6aba7d23-1605-4d40-b3bd-a5374c813f44

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

Record type: Article

Abstract

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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Published date: 2005
Organisations: Southampton Wireless Group

Identifiers

Local EPrints ID: 262195
URI: https://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: 16 Jul 2019 22:45

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