Journal
SYSTEMS & CONTROL LETTERS
Volume 54, Issue 4, Pages 325-329Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.sysconle.2004.09.003
Keywords
bahavioral systems; persistency of excitation; lags; annihilators; system identification
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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. (C) 2004 Elsevier B.V. All rights reserved.
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