Weak observability and observers for linear neutral delay-differential systems

Observability concepts and observers are discussed for linear neutral delay-differential systems, according to an algebraic approach (ring theory). For delay systems of retarded type, various schemes for developing exact and asymptotic observers may be found in [5] and [9]. We investigate here the procedures for the extension to the neutral case. Let us mention that the proofs to derive the necessary and sufficient conditions for systems over a ring (or for delay-differential systems) to be detectable are not constructive inasmuch as they do not explicit any state observers for these systems (see for instance [2], [3]). The methods derived in this paper then appear as an alternative which actually leads to the observation of the retarded state, this observation being effective modulo some internal delays of the system. Moreover, an original model, which includes the initial conditions, is presented.