On Eigenstructure Assignment by Gain Output Feedback

Abstract

In this paper, the eigenstructure assignment of linear multivariable control systems is studied from a geometric point of view. For the class of systems in which the number of outputs plus the number of inputs exceeds the number of states, genericity properties relative to this problem are derived. It is shown, without any assumption on the genericity of the system, that the pole assignment can be carried out by choosing some closed-loop eigenvectors almost freely. The crucial point is that all the expected degrees of freedom in pole assignment are so described without redundancy, which fully justifies the practical interest of such techniques. Despite the technicality required for the derivation of intermediate results, the main result, which is an eigenstructure assignment algorithm, is very easy to implement because it is only based on the computation of certain sums and intersections of characteristic subspaces. Furthermore, it is shown how the basic tools developed here can be used to tackle the problem of finding a necessary and sufficient condition for exact pole assignment.