International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 55, Pages 3519-3538

Integral observability operators of nonlinear dynamical systems

Yury V. Zaika

Institute of Applied Mathematical Research, Karelian Research Center, Russian Academy of Sciences, Petrozavodsk 185610, Russia

Received 25 March 2002

Copyright © 2003 Yury V. Zaika. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In terms of functional dependence, the description of observable functions in nonlinear dynamical systems, which are analytic with respect to phase variables, is obtained. For processing of measurements, integral operators are used, which provide certain noise stability of operation of phase state reconstruction. The analogue of the duality theory known for linear problems of observation and control is developed. Computing schemes for nonlinear observability problem are proposed.