Section: New Results

Interval Observer

Participants : Frédéric Mazenc [correspondent] , Thach Ngoc Dinh, Silviu Iulian Niculescu.

We made several progresses in the domain of the construction of state estimators called interval observers.

1) In [18] , we have shown how interval observers can be constructed for nonlinear (and not Lipschitz) systems possessing a special triangular system.

2) The contributions [20] and [55] present a new major result for the design of interval observers for discete-time systems with input and output: it is explained how two classical Luenberger obsevers can be used, even in the absence of the positivity property as interval observer, provided two appropriate output, which compose the lower and the upper bound of the interval observer, are selected. In [19] , coordinate transformations which change an arbitrary linear discrete-time system into a positive one and general nonlinear design of interval observers for nonlinear systems (satisfying a restricitive stability assumption) are proposed.

3) The paper [54] presents the first construction of continuous-discrete interval observer for linear continuous-time systems with discrete measurements. The importance in engineering applications of this result is clear: most of the time the measured variables are available at discrete instants only. The result relies on the design of changes of coordinates which transform a linear system into a nonnegative one, but the dynamic part of interval observers is not cooperative.