Parametric eigenstructure assignment for descriptor systems via proportional plus derivative state feedback

Eigenstructure assignment for descriptor systems with proportional plus derivative state feedback is studied. Based on a simple complete explicit parametric solution to a group of recursive equations, a parametric approach for eigenstrucure assignment in descriptor systems via proportional plus derivative state feedback is proposed. The proposed approach possesses the following features: 1) it does not impose any condition on the closed-loop eigenvalues, simultaneously assigns arbitrary n finite and infinite eigenvalues to the closed-loop system and guarantees the closed-loop regularity; 2) it is simple and needs less computational work; 3) it gives general complete parametric expressions for the closed-loop eigenvectors, the proportional state feedback gain matrix and the derivative state feedback gain matrix.