Partial Eigenstructure assignment for descriptor linear systems: a complete parametric approach

This paper investigates the problem of partial eigenstructure assignment (PESA) by state feedback in R-controllable, time-invariant descriptor linear systems. Simple, complete, parametric solutions to PESA are obtained. Two special cases are especially examined, one is replacing a single real eigenvalue and its corresponding eigenvector, the other is replacing a pair of conjugate eigenvalues together with their eigenvectors. Based one these results, a circulation method for PESA is developed, which does not involve inverses of matrices. The parameter vectors in the proposed solutions give all the degrees of design freedom which can be further utilized to achieve additional system specifications. A numerical example shows the effect of the proposed approach.