A Unified Constructive Study of Linear, Nonlinear and Discrete Event Systems
1995 (English)Report (Other academic)
Starting from the behavioral point of view a system is defined by its set of behaviors. In discrete time this is a relation over D N and hence a very infinite object. A model is a relation over D N for some finite N that can be extended to a behavior. Furthermore properties of a system is defined in terms of its behavior. Starting from a constructive point of view we need to be able to represent and manipulate systems. A natural choice is to use some a constructive model, i.e. one that can be finitely represented and manipulated. We will consider four such classes of models: polynomial and linear relations over finite and infinite fields. There are a number of restrictions on the geometric (or behavioral) operations that are possible for each of these classes and still remain within the class. If we want to interpret our models as systems and analyze system properties, then several properties become impossible to compute. Some examples: The set of reachable states for a polynomial model over an infinite field is in general impossible to compute. It may converge to be fractal. The set of reacable states ik steps or less in a linear model cannot be represented as a linear set in general.
Place, publisher, year, edition, pages
1995. , 17 p.
LiTH-ISY-R, ISSN 1400-3902 ; 1748
Nonlinear systems, Discrete event systems, Constructive methods
IdentifiersURN: urn:nbn:se:liu:diva-55258ISRN: LiTH-ISY-R-1748OAI: oai:DiVA.org:liu-55258DiVA: diva2:315879
FunderSwedish Research Council