Applications of Gröbner Bases to Nonlinear Systems
1991 (English)In: Proceedings of the First European Control Conference, 1991, 164-169 p.Conference paper (Refereed)
Some problems within nonlinear control theory are stated and solved using so called Gröbner bases from commutative algebra. The first problem is the one of stability and performance robustness of nonlinear systems subject to structured uncertainty. It is assumed that a Lyapunov function is given, and the quality of the solution depends on this Lyapunov function. It is also indicated how the robustness problem can be reinterpreted in different ways, e.g. in terms of controller design. The second problem is the one of finding a differential equation connecting the input and the output of a system starting form a state space description of it. In all cases the nonlinearities are required to be of polynomial type. The methods suggested are illustrated with concrete examples.
Place, publisher, year, edition, pages
1991. 164-169 p.
Nonlinear control systems, Commutative algebra, Lyapunov theory, Stability robustness, Performance robustness, State space equation
IdentifiersURN: urn:nbn:se:liu:diva-91667ISBN: 978-2866012809OAI: oai:DiVA.org:liu-91667DiVA: diva2:618471
First European Control Conference, Grenoble, France, July, 1991