Generalized PID Observer Design for Descriptor Linear Systems

A type of generalized proportional-integral-derivative observers is proposed for descriptor linear systems. Based on a general parametric solution to a type of generalized Sylvester matrix equations, a parametric design approach for such observers is established. The proposed approach provides 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. In addition, a numerical example is employed to show the design procedure and illustrate the effect of the presented approach.