Recent developments in eigenvalue-eigenspace assignment

Abstract

Response characteristics of a linear state feed-back controller are reflected indirectly by the closed loop eigenstructure, and it is possible to impose constraints on this structure. These constraints define a class of matrices, and unless it has a unique member, one is faced with computing a "good" feedback matrix. In this paper we address two aspects of this problem which allow direct application of numerical analysis work. Essentially, there are two ideas which are discussed 1) If the closed loop eigenvalues are separated, one should avoid a closed loop system whose eigenvector matrix is nearly singular. 2) If there are to be repeated or clustered eigenvalues, one should not deal directly with the eigenvectors of the cluster; instead one should use an orthogonal basis which approximates the corresponding closed loop (A+BF) invariant subspace.