Sufficient conditions for viability under imperfect measurement

Viability theory gives a necessary and sufficient condition for the existence of a (set-valued) state feedback control such that all trajectories of the closed-loop system starting from the graph of a given tube in the state space remain in the tube. Here we investigate the same problem in the case where only incomplete and inexact measurement of the state is available. In the time-invariant case, we give a sufficient condition for the existence of anoutput feedback regulation map. The condition is shown to be equivalent to Haddad's viability condition if the measurement is perfect.