Section: New Results

Interval Observers

Participants : Frédéric Mazenc, Siviu Niculescu, Olivier Bernard [UNICAMP] .

The technique, based on the notion of interval observer, is a recent state estimation technique, which offers the advantage of providing information on the current state of a system at any instant of time. The firts interval observers where relying on the assumption that the system was cooperative or, roughly speaking, "almost" cooperative.

In the contribution [25] , we have proved that, for any time-invariant exponentially stable linear system with additive disturbances, time-varying exponentially stable interval observers can be constructed. The technique of construction relies on the Jordan canonical form that any real matrix admits and on time-varying changes of coordinates for elementary Jordan blocks which lead to cooperative linear systems. We applied our to the case of linear systems with input and output that are detectable.

The paper [31] focused on the analysis and the design of families of interval observers for linear systems with a point-wise delay. First, we proved that classical interval observers for systems without delays are not robust with respect to the presence of delays, no matter how small delays are. Next, we have shown that, in general, for linear systems with delay, the classical interval observers endowed with a point-wise delay are unstable. A new type of design of interval observers enabling to circumvent these obstacles is proposed. It provides with framers that incorporate distributed delay terms. The proposed interval observers are assessed through a non-linear biotechnological model.