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Geometric and algebraic properties of minimal bases of singular systems

Karcanias, N. (2013). Geometric and algebraic properties of minimal bases of singular systems. International Journal of Control, 86(11), pp. 1924-1945. doi: 10.1080/00207179.2013.816869


For a general singular system with an associated pencil T(S), a complete classification of the right polynomial vector pairs x(s), u(s)), connected with the N{script}r{T(S)}, rational vector space, is given according to the proper-nonproper property, characterising the relationship of the degrees of those two vectors. An integral part of the classification of right pairs is the development of the notions of canonical and normal minimal bases for N{script}r{T(S)} and N{script}r{R(S)} rational vector spaces, where R(s) is the state restriction pencil of Se[E, A, B]. It is shown that the notions of canonical and normal minimal bases are equivalent; the first notion characterises the pure algebraic aspect of the classification, whereas the second is intimately connected to the real geometry properties and the underlying generation mechanism of the proper and nonproper state vectors x(s). The results describe the algebraic and geometric dimensions of the invariant partitioning of the set of reachability indices of singular systems. The classification of all proper and nonproper polynomial vectors x(s) induces a corresponding classification for the reachability spaces to proper-nonproper and results related to the possible dimensions feedback-spectra assignment properties of them are also given. The classification of minimal bases introduces new feedback invariants for singular systems, based on the real geometry of polynomial minimal bases, and provides an extension of the standard theory for proper systems (Warren, M.E., & Eckenberg, A.E. (1975).

Publication Type: Article
Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in International Journal of Control on 22 Aug 2013, available online:
Publisher Keywords: singular systems, algebraic systems theory
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Engineering
SWORD Depositor:
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