Optimal pole shifting for discrete multivariable systems

Abstract

A method for shifting the open-loop eigenvalues by a proportion of 1/δ is presented. In each step of the method it is required to solve a first-order or a second-order matrix equation for shifting one real pole or two complex conjugate poles, respectively. The presented method yields a solution which is optimal with respect to a quadratic performance index. One of the two attractive features of the method is that it can be easily applied to large-scale systems without solving any large order matrix equations. The second feature is its recursive nature which makes it applicable to open-loop systems with multiple eigenvalues.