LOCAL OBSERVABILITY OF INVARIANT DYNAMICS ON COMPACT LIE-GROUPS WITH SQUARE INTEGRABLE OUTPUT MAP FUNCTIONS

In this work, we give a sufficient algebraic condition for the local o bservability problem of invariant control systems on compact Lie group s such that the output map is not differentiable. In particular, the u sual techniques involving Lie derivatives do not work. Our approach co mes from the representation theory. We use the regular representation to construct a bilinear system on the Hilbert space of the square inte grable function defined on the group to a finite-dimensional vector sp ace. If this bilinear system is observable, then we prove that the inv ariant control system is locally observable.