15th Triennial World Congress of the International Federation of Automatic Control
  Barcelona, 21–26 July 2002 
UNCERTAIN SYSTEMS, BEHAVIOURS AND QUADRATIC DIFFERENTIAL FORMS
Ian R. Petersen* Jan C. Willems**
* School of Electrical Engineering, Australian Defence Force Academy,
Campbell, 2600, Australia, Phone +61 2
62688446, FAX +61 2 62688443, email: irp@ee.adfa.oz.au
** Research Institute for Mathematics and Computing Science, P.O. Box
800, 9700 AV Groningen, The Netherlands

This paper considers uncertain systems from a behavioural point of view defined via quadratic differential forms. This uncertainty definition is closely related to the integral quadratic constraint uncertainty description commonly found in robust control theory. The paper presents a frequency domain condition for the set of behaviours of a given uncertain system to contain the set of behaviours of another given uncertain system. This result is useful in uncertainty modelling problems in which one wishes to consider the trade off between model complexity and model conservatism.
Keywords: Uncertain Systems; Behaviours; Quadratic Differential Forms; Equivalent Realizations; Uncertainty Modelling; Differential Inequality Systems
Session slot T-Fr-A15: Uncertain Systems/Area code 2e : Robust Control