Design of observer-based compensators in the frequency domain: the discrete-time case

Abstract

For nth order systems with m outputs, the design of compensators using state observers of order n − x with 0 ≤ x ≥ m is presented in the z-domain. The design is carried out in equivalence with the usual time-domain approach and the relations between the time- and the frequency-domain results are presented. The state feedback and the observer are characterized by polynomial matrices in the frequency domain and the corresponding compensator matrix fraction descriptions are obtained from the solution of a linear diophantine equation. In view of the optimal state-estimation problem, the use of an updated state estimate is of interest. It is shown how this problem can also be solved in the frequency domain.