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

A kind of full-order proportional-integral observers is proposed for linear discrete time-delay systems, which possesses the separation property. The existence condition of such a kind of observer is presented. A parametric design approach is established based on a general parametric solution of the generalized Sylvester matrix equation. This approach provides not only complete parameterization of all the observer gain matrices but also the parametric expression of left eigenvector matrix of the observer system. All the degree of design freedom is offered, and convenient and powerful tools are supplied to achieve other performance specifications. Numerical example shows the design procedure and the effectiveness of the proposed approach.