Eigenvalue/eigenvector assignment by state-feedback

Abstract

The problem of simultaneous assignment of closed-loop eigenvalues and eigenvectors using constant complete state-feedback controller is discussed. It is shown that for a given nth-order multivariable system not necessarily completely controllable, associated with every point. λ in the complex plane, there exists a well-defined subspace (in the n-dimensional vector space) within which the eigenvector v corresponding to the eigenvalue at A must lie in order for a real valued controller. assigning the pair (λ, v), to exist. This sub-space is completely determined by the given system and λ. Based on this fact, a necessary and sufficient condition for k pairs of desired closed-loop eigenvalues-eigenvectors, where 1≤κ≤n, to be simultaneously assignable by state-feedback is proposed and a method for determining a controller to assign them is presented. The method is applicable to the case of linearly independent eigenvectors with distinct or repeated eigenvalues as well as that of multiple eigenvectors