Observer Design in Infinite-dimensional Setting Using Delayed Measurements

An asymptotic observer for a linear system, evolving in a Hilbert space, is designed over linear state measurements with time-varying delays. The proposed predictor-based approach reduces the problem to the standard one with non-delayed information on the state, thereby being invariant to the dimensionality of the underlying system. Capabilities of the resulting observer design are illustrated for the linearized Kuramoto-Sivashinsky PDE with periodic boundary conditions and with delayed finite-dimensional measurements.