Parametric approaches for observer design in high-order descriptor linear systems

This paper considers the problem of observer design in high-order descriptor linear systems. Parametric expressions for the left eigenvectors associated with the finite eigenvalues of the observer and simple and complete parametric solutions for the observer gain matrices are obtained on the basis of the parametric solution of the generalized high-order Sylvester matrix equation. This approach does not impose any restriction on the observer eigenvalues. An illustrative example shows the effect of the proposed approaches.