Pole assignment problem: a structural investigation

Based on the structure of a closed-loop system under a specified feedback pattern, a qualitative analysis of the problem of pole assignability is considered. The problem is first formulated algebraically, in terms of the relation p = g(f) between the vector p of the closed-loop characteristic polynomial coefficients and the vector f of the non-zero elements of the feedback matrix. Then, translation to the structural framework is achieved by means of two theorems which give graph-theoretical sufficient conditions for solvability. These structural conditions also guarantee genericity of pole assignability.