Parametric eigenvalue assignment by constant output feedback – a cascaded approach

Abstract

Abstract In this paper a numerical efficient approach to the problem of eigenvalue assignment by constant output feedback is presented. It improves the well known Kimura’s condition by 2, i. e., it is shown that if m + p ≥ n − 1 m+p\ge n-1 generically a solution to this design problem exists where n , m n,m and p denote the dimensions of the system states, inputs and outputs, respectively. The algorithm is based on a cascaded control scheme with up to three design steps. The first two steps merely require standard methods from linear algebra while the last step only in case of m + p = n − 1 m+p=n-1 demands for the numerical solution of a system of three polynomial equations each of order two. The design procedure explicitly embodies all degrees of freedom beyond eigenvalue assignment. Thus, they can be used to account for other design it is shown goals, e. g., to minimize the spectral condition number of the closed-loop system or a norm of the feedback gain as it is shown by numerical examples from literature.