Autonomous behaviours decomposition and modal analysis

Authors: Bisiacco M.; Valcher M.E.

Source: International Journal of Control, Volume 74, Number 17, 20 November 2001 , pp. 1690-1705(16)

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Abstract:

In this paper, the notions of simple, very simple and indecomposable autonomous behaviour are introduced and characterized. By resorting to some recent results about the direct sum decomposition of (linear, time-invariant, differential) 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 expressed as a direct sum of indecomposable components, which are just cyclic modules of order p^v, for some irreducible polynomial p and some positive integer v. The non-uniqueness of this result is also discussed. Finally, this 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 the behaviour.

Language: English

Document Type: Research article

Publication date: 2001-11-20

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