Design of observers with disturbance decoupling in descriptor systems

A sufficient and necessary condition for Luenberger function observers with disturbance decoupling in descriptor systems is established. Based on this constraint and an explicit general solution to a type of generalized Sylvester matrix equations, a parametric design approach for Luenberger observers with disturbance decoupling is proposed. The proposed approach first gives the parameterizations of all the observer gains and then a design algorithm for the type of observers with disturbance decoupling by combining the parameterizations of the observer gain matrices and the proposed condition for disturbance decoupling. A numerical example illustrates the effect of the proposed approach.