Design of PI observers for continuous-time descriptor linear systems

A parametric design approach for proportional-integral (PI) observers for continuous-time descriptor linear systems is proposed based on a complete general parametric solution to the generalized Sylvester matrix equation. The proposed approach provides complete parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding finite left eigenvector matrix of the observer system matrix, realizes elimination of impulsive responses, and guarantees the regularity of the observer system. The design method offers all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances and, thus, has great potentials in applications. A numerical example is employed to show the design procedure and illustrate the effect of the proposed approach. Simulation results show a satisfactory tracking performance for descriptor linear systems.