Autonomous behaviours decomposition and modal analysis

Citation
M. Bisiacco et Me. Valcher, Autonomous behaviours decomposition and modal analysis, INT J CONTR, 74(17), 2001, pp. 1690-1705
Citations number
11
Categorie Soggetti
AI Robotics and Automatic Control
Journal title
INTERNATIONAL JOURNAL OF CONTROL
ISSN journal
00207179 → ACNP
Volume
74
Issue
17
Year of publication
2001
Pages
1690 - 1705
Database
ISI
SICI code
0020-7179(200111)74:17<1690:ABDAMA>2.0.ZU;2-1
Abstract
In this paper, the notions of simple, very simple and indecomposable autono mous behaviour are introduced and characterized. By resorting to some recen t results about the direct sum decomposition of (linear, time-invariant, di fferential) behaviours (Bisiacco and Valcher 2001), as well as to the well- known primary decomposition theorem for finitely generated modules (Hartley and Hawkes 1970), it is shown that every autonomous behaviour can be expre ssed as a direct sum of indecomposable components, which are just cyclic mo dules of order p(nu), for some irreducible polynomial p and some positive i nteger nu. The non-uniqueness of this result is also discussed. Finally, th is decomposition is interpreted in terms of modal analysis, and related to the results that can be obtained by mean of a state-space realization of th e behaviour.