Using Differential and Real Algebra in Control
1999 (English)In: Symbolic Methods in Control System Analysis and Design / [ed] Neil Munro, London: Institution of Electrical Engineers (IEE), 1999, 115-134 p.Chapter in book (Other academic)
In the analysis of linear systems algebraic methods have been important since the early work of Routh and Hurwitz. Much of the work has been concerned with transfer functions or transfer matrices. For nonlinear systems the use of algebraic methods was for a long time made difficult by the complexity of the calculations involved. In recent years the availability of symbolic computer based methods has made it possible to explore algebraic methods in the nonlinear context. Here we concentrate on two approaches: differential algebra, which can be used to eliminate variables in systems of differential equations, and real algebra, which gives computational tools to handle systems of polynomial equations and inequalities. We give very brief overviews of the computational algorithms and then present some control related applications. To begin with we also note that the restriction to polynomial systems is not very severe. It can be shown that systems where the nonlinearities are not originally polynomial may be rewritten in polynomial form if the nonlinearities themselves are solutions to algebraic differential equations.
Place, publisher, year, edition, pages
London: Institution of Electrical Engineers (IEE), 1999. 115-134 p.
Differential algebra, Real algebra, Symbolic methods, Linear systems, Control theory
IdentifiersURN: urn:nbn:se:liu:diva-56318DOI: 10.1049/PBCE056E_ch5ISBN: 0-85296-943-0OAI: oai:DiVA.org:liu-56318DiVA: diva2:318422