Design of Generalized PI Observers for Descriptor Linear Systems

The new type of generalized proportional integral (GPI) observers for descriptor linear systems is proposed. Based on a complete parametric solution to a type of generalized Sylvester matrix equations, a parametric approach for the design of the GPI observers is established. The proposed approach gives parameterizations of all the observer gain matrices in terms of some free parameters which represent the degrees of design freedom. Moreover, the parametric expression of the corresponding finite left eigenvector matrix of the observer system is also presented. The proposed approach, which guarantees the regularity of the observer system, realizes the elimination of impulsive behaviors of the observer system. The proposed design method offers all the degrees of design freedom which can be further utilized to achieve additional specifications and performances. An illustrative example shows the effect of the proposed approach