Eigenstructure Assignment by State Feedback

The problem of simulataneous assignment of a set of closed loop eigenvalues and eigenvectors using state feedback is discussed. For mutivariable systems, the non-uniqueness of the state feedback gain for assigning a set of eigenvalues of a multivariable system provides the designer freedom in the selection of closed loop eigenvectors. An efficient method for the computation of a basis of the subspace of assignable closed loop eigenbectors is presented. A new necessary and sufficient condition for the simulataneous assignment of partial or entire eigenvalues and eigenvectors is derived. A numerical example is given to illustrate the results.