Observer design in the presence of periodic output disturbances by mixing of past and present output data

We consider the problem of observer design for systems with periodic disturbances in the system outputs. Assuming that the period T of the disturbance is known, we introduce the idea of mixing past and present output data to remove the disturbance, by defining a new output as the difference between the original output at time t and at time t-T .We determine the exact conditions under which the system is observable from the redefined output, and specify how to design an observer using regular pole-placement techniques and linear time-invariant analysis. We validate the design through simulations.