PARAMETRIC MULTIPLE EIGENVALUE SHIFTING WITH MINIMUM EIGEN-VALUE SENSITIVITY VIA STATE-FEEDBACK BASED ON BLOCK SCHUR FORM

Abstract

Based on the block Schur form of an open-loop system matrix, a new sequential design procedure is proposed for characterizing an explicit parametric class of linear state-feedback controllers for the open-loop system, which will shift an arbitrary prescribed spectrum of distinct self-conjugate multiple eigenvalues to the closed-loop system. We also consider the problem of minimizing the sensitivity of the shifted closed-loop multiple eigenvalues with respect to parameter variations in all elements of the closed-loop plant matrix. An insightful parameterization of the desirable closed-loop multiple eigenvalue sensitivity is provided through the explicit parametric class of linear state-feedback controllers. Based on this parameterization, a least square method for designing a state-feedback gain matrix which shifts a desirable set of distinct closed-loop multiple eigenvalues, such that these multiple eigenvalues have minimum sensitivity to perturbation in the closed-loop plant matrix, is presented. A numerical example is worked out to illustrate the design procedures.