Recursive eigenstructure assignment in linear systems

In Arbel and Rath (1985) an iterative eigenvalue assignment algorithm was presented. This algorithm has the shortcomings of clustering most of the closed-loop eigenvalues on the real axis. A general method is given here for recursive eigenstructure assignment in linear systems. The method eliminates the shortcomings of the algorithm of Arbel and Rath. It is shown that the right and left eigenvectors of the closed-loop system matrix can be determined in terms of those of a small-dimension matrix A?_c . It is also shown that the results of Arbel and Tse (1980) are special cases of those of the proposed method. Moreover, the arbitrary parameters, beyond eigenvalue assignment, are shown to be embedded in the choice of a certain arbitrary invertible matrix S. Furthermore, computer-oriented steps are outlined for recursive eigenstructure assignment in large-scale systems. Numerical examples are worked out to illustrate the generality and feasibility of the proposed method.