Observability for any input: a canonical form for mimo systems

A canonical form characterizing systems that are observable for any input is firstly proposed. Then, the synthesis of a high gain observer for these systems is detailed. The proposed class of systems is particularly composed by cascade subsystems where each subsystem is associated to a subset of the output variables and assumes a triangular dependence on its own state variables and may depend on the state variables of all other subsystems. The main contribution consists in extending the available results to allow more interconnections between the subsystems. Of fundamental interest, it is shown that he underlying observation error exponentially converges to zero in the absence of uncertainties. Moreover, the observation error can be made as small as desired by properly specifying the observer design parameter in the case where uncertainties are considered.