Necessary and sufficient conditions for the existence and design of disturbance decoupled reduced-order observers for continuous linear descriptor systems are presented. The observer existence conditions are based on the solution of a generalized Sylvester's equation, under a constraint that describes the disturbance decoupling of the estimated state, and on a rank condition that guarantees the existence of matrices for the reconstruction of all state variables, also with disturbance decoupling. Basically, the design conditions of the desired observer are associated to some structural properties of the descriptor system. From these results, we propose an observer design algorithm that is based on eigenstructure assignment technique. The presented results are useful when an estimated state feedback control law is considered. An illustrative numerical example is reported.
Descriptor Systems; Observers; Minimal order; Sylvester's equation; Eigenstructure assignment
