Mathematical Problems in Engineering
Volume 6 (2000), Issue 1, Pages 31-60

Robust high-gain observer for nonlinear closed-loop stochastic systems

A. S. Poznyak,1,2 R. Martínez-Guerra,1 and A. Osorio-Cordero1

1Cinvestav-Ipn, Automatic Control Department, A.P.14-740, Mexico D.F. CP 07360, Mexico
2Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence 66045, KS, USA

Received 13 September 1999; Revised 29 October 1999

Copyright © 2000 A. S. Poznyak et al. 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 this paper, the problem of robust state observation is tackled. A high-gain observer is employed to carry out the state estimation of a continuous time uncertain nonlinear system subject to external perturbations of stochastic nature. Unmodelled dynamics is assumed to be deterministic and belonging to an a priori known class of uncertainties.The control input is constructed based on the state estimates supplied by this observer. An upper bound for the estimation error and the states of this closed-loop system is derived. It is shown to be a linear combination of all a priori given uncertainty levels and turns out to be “tight” (reachable). The proposed scheme is applied to a robot manipulator with unknown friction and inaccessible angular velocities.