Design of proportional-integral observers for discrete-time descriptor linear systems

A type of proportional-integral observers for discrete-time linear systems is proposed. Based on a complete parametric solution to the generalised Sylvester matrix equation, a parametric design approach for such a type of observers is proposed. The proposed approach provides all the gain matrices of the observer, gives the parametric expression for the corresponding finite left eigenvector matrix of the observer system matrix and guarantees the regularity of the observer system. A numerical example is provided to show the design procedure and illustrate the effectiveness of the proposed approach.