High gain observers based on immersion technics

The high gain observer based on normal forms is initially proposed in. These normal forms characterize single input uniformly observable systems (systems which are observable independently on the input). Next, in, this observable normal form together with observer synthesis have been extended to a class of MIMO nonlinear systems by assuming that some regular flag of co-distribution does not depend on the input. In this paper, the regularity hypothesis of the above flag of co-distribution is omitted and an immersion (embedding map) is proposed in order to transform a nonlinear system into a normal form defined on a higher dimensional state space.