ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

17. Control Theory and Optimization

1991 MS Classification: 93 Bartosiewicz, Zbigniew, Politechnika Białostocka, Poland Local observability, ideals and finiteness conditions Let I_{x_{0}} be the ideal generated by germs of functions vanishing at x_{0} from the observation algebra of an analytic control system on R^{n}. The system is locally observable at x_{0} iff the real radical of I_{x_{0}} is maximal. If real radical is replaced by ordinary radical, the condition of maximality gets stronger. It is equivalent to a finiteness condition considered by Gauthier and Jouan, which implies that observation algebra is finitely analytically generated at x_{0}. Thus maximality of the ordinary radical of I_{x_{0}} gives both local observability and finite analytic generatedness. On the other hand, maximality of the real radical of I_{x_{0}} is too weak to guarantee finite analytic generatedness of the observation algebra.