Nonlinear observer design in the presence of delayed output measurements

The present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements. The proposed nonlinear observer possesses a state-dependent gain which is computed from the solution of a system of first-order singular partial differential equations, and in particular, consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time-instants within the time-delay window introduced by the available output measurements. Therefore, the proposed nonlinear observer exhibits a chain-like structure that explicitly reflects and takes into account the magnitude of the output delay. Furthermore, a set of conditions is derived under which convergence of the estimation error to zero is established. Finally, the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example.