Continuous-discrete time observers for a class of MIMO nonlinear systems
Résumé
The observer design problem for nonlinear
dynamical systems has received a remarkable attention over the
last four decades. A considerable effort has been devoted to the
observer design for systems that are observable for any input
using the high gain concept for exponential convergence purposes.
It is however worth mentioning that the available results are
mainly devoted to the continuous-time measurements case in spite
of some nice contributions concerning the sampled measurements
case. The motivation of this talk consists in addressing the
problem of redesigning a high gain continuous-time observer for a
class of MIMO nonlinear systems that are observable for any input
in the case of non uniformly sampled measurements. This provides a
high gain continuous-discrete time observer witch is more suitable
from an engineering practice point of view. Two design features of
the proposed continuous-discrete time observer are worth to be
pointed out. Firstly, the observer is particularly described by a
set of differential equations with instantaneous state impulses
corresponding to the measured samples and their estimates and is
hence an impulsive system in nature. Secondly, the involved
observer gain is time-varying and its calibration is achieved
throughout the tuning of two design parameters. A particular
emphasis in put on the exponential convergence of the observer
provided that the sampling process is not too fast in a well
defined sense. Moreover, a suitable interpretation of the proposed
continuous-discrete time observer is given, namely it is shown
that the underlying impulsive system can be put under the form of
a hybrid system witch is synthesized using a continuous-time
design with an inter sample output predictor. The effectiveness of
the proposed continuous-discrete time observer is emphasized
throughout simulation results involving useful observer design
problems.