Impulsive observer design for a class of continuous biological reactors

The problem of state estimation for a class of continuous bioreactors with sampled biased measurements with nonperiodic rates is addressed within the framework of impulsive dynamical systems. Explicit conditions on the maximum time between measurements are established which ensure input-to-state stability of the estimation error with respect to the measurement uncertainty and, additionally, finitetime practical stability of the estimation error. The theoretical results are illustrated on the case study of a reactor with nonmonotonic reaction rate for which the state is not observable from continuous time measurements but only detectable.