Polynomial systems theory applied to the analysis and design of multidimensional systems

• Autorzy: Hatonen J. , Ylinen R.
• Języki publikacji: EN

Abstrakty

EN

The use of a principal ideal domain structure for the analysis and design of multidimensional systems is discussed. As a first step it is shown that a lattice structure can be introduced for IO-relations generated by polynomial matrices in a signal space X (an Abelian group). It is assumed that the matrices take values in a polynomial ring F[p] where F is a field such that F[p] is a commutative subring of the ring of endomorphisms of X. After that it is analysed when a given F[p] acting on X can be extended to its field of fractions F(p). The conditions on the pair (F[p],X) are quite restrictive, i.e. each non-zero a(p)\in F[p] has to be an automorphism on X before the extension is possible. However, when this condition is met, say for operators { p1,p2,..., pn-1}, a polynomial ring F[p1,p2,...,pn] acting on X can be extended to F(p1,p2,..., pn-1)[pn], resulting in a principal ideal domain structure. Hence in this case all the rigorous principles of `ordinary' polynomial systems theory for the analysis and design of systems is applicable. As an example, both an observer for estimating non-measurable outputs and a stabilizing controller for a distributed parameter system are designed.

Słowa kluczowe

EN

nD systems; module of fractions; partial differential equations; polynomial systems theory

PL

moduł frakcji; równanie różniczkowe cząstkowe; teoria układów wielomianowych

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2003
• Tom: Vol. 13, no 1
• Strony: 15--27
• Opis fizyczny: Bibliogr. 18 poz., rys., wykr.

Twórcy

autor

Hatonen J.

• University of Oulu, Systems Engineering Laboratory, P.O. Box 4300, FIN-90014, Finland

autor

Ylinen R.

• University of Oulu, Systems Engineering Laboratory, P.O. Box 4300, FIN-90014, Finland

Bibliografia

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