5 CONCLUSION
The main contribution of this paper is the
development of a dynamic output feedback based
observer that will be referred to as a CRONE
observer in future developments. This name results
in the introduction of CRONE controller in a
feedback loop whose goal is to cancel the error
between a model state and the unmeasured state of a
plant that must be estimated. State observation with
a dynamic output feedback based observer is
concept that was developed in two papers (Marquez,
2003) and (Marquez and Riaz, 2005). Such an
approach of state observation permits:

a generalisation of the Luenberger form
(Luenberger, 1971) that thus allows more
freedom and flexibility in the design,

a formulation allowing a more transparent view
of the observer properties in term of feedback
elements

to poses the disturbances rejection problem and
the observation robustness problem in the
context of robust control theory.
The main differences between this paper and
(Marquez, 2003) and (Marquez and Riaz, 2005) are :

the extension of the dynamic output feedback
based observer idea to the observation problem
with unknown input,

the uses of a CRONE controller to solve the
disturbances rejection problem and the
observation robustness (robustness of the
observation error convergence to zero).
With the CRONE controller, plant model
perturbations are taken into account in a structured
form with no overestimation (but unmodelled
dynamics can also be taken into account). Thus,
without conservatism introduced in the plant
uncertainties modelling, and in spite of a global
optimization proof lack of the non convex
optimisation problem defined in CRONE control, it
turn out that in practice a CRONE controller permits
to obtain better performance than an H
∞
one on the
same plants (see for instance (Landau, et al, 1995)
for a comparison on a benchmark based on robust
digital control of a flexible transmission system).
Due to the introduction of fractional differentiation,
a parameterization of the open loop transfer function
with a small number of parameters (three just like a
PID controller) is obtained. The optimisation of the
control law is thus reduced to the search for the
optimal values of these parameters.
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