PMID Observer Design of Descriptor Linear Systems

A new type of observers for descriptor linear systems, proportional multiple-integral derivative (PMID) observers, is proposed. Based on a general parametric solution to a type of generalized Sylvester matrix equations, a parametric approach for designing such observers is proposed. The proposed approach establishes the complete parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes the elimination of impulsive behaviors, and guarantees the regularity of the observer system. The design method can offer all the degrees of design freedom which can be utilized to achieve various desired system specifications and performances.