EIGENSTRUCTURE ASSIGNMENT IN DESCRIPTOR SYSTEMS VIA STATE-FEEDBACK - A NEW COMPLETE PARAMETRIC APPROACH

A new complete parametric approach for eigenstructure assignment in co ntrollable linear descriptor systems, Ex = Ax + Bu via the static stat e feedback control u = Kx, is proposed. General complete parametric ex pressions in direct closed forms for the closed-loop eigenvectors asso ciated with the finite closed-loop eigenvalues are presented based on a recently proposed complete parametric solution to the generalized Sy lvester matrix equation AV + BW = EVF. These expressions are linear in a group of parameter vectors which represent the degree of the design freedom. A very simple complete parametric solution for the feedback gain matrix K is also established with the help of a proposed 'complet ing the square' technique. The approach guarantees arbitral assignment of rank(E) number finite closed-loop eigenvalues with arbitrary given algebraic and geometric multiplicities, and realizes elimination of a ll possible initial time impulsive responses. It also guarantees the c losed-loop regularity when two simple constraints on the design parame ters are added. The approach does not impose any condition on the clos ed-loop finite eigenvalues, and over comes the drawback of some previo us work. Two examples illustrate the advantages of the proposed approa ch.