Exponentially Stable Interval Observers for Linear Systems with Delay

This paper focuses on the analysis and the design of families of interval observers for linear systems with a point-wise delay. First, it is 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, it is 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.