Implicitization, Graph Ideals and Control Systems
1993 (English)Report (Other academic)
We discuss how the external behavior of a polynomial automatic control system can be determined, i.e. how to find the differential equation relating the input and the output of the system given a state space description, focussing on algorithmic aspects. This problem is equivalent to what is known as implicitization in computational algebraic geometry and one way of doing this is to perform elimination in so called graph ideals. We compare different methods for implicitization with regard to computational complexity. Moreover, a bound for the degree of the input-output equation in terms of the degrees of the state equations is derived.
Place, publisher, year, edition, pages
Linköping: Linköping University , 1993. , 8 p.
LiTH-ISY-R, ISSN 1400-3902 ; 1508
Control systems, State space theory, Algebraic geometry, Implicitization, Bézout's theorem, Computer algebra, Symbolic computation, Elimination, Gröbner bases, Computational complexity
IdentifiersURN: urn:nbn:se:liu:diva-55601ISRN: LiTH-ISY-R-1508OAI: oai:DiVA.org:liu-55601DiVA: diva2:316314