A structural analysis of the characteristic equation of an output feedback system

Recent studies in pole placement have investigated the degree of flexibility available when feedback is constrained to constant gains on the output variables of a linear system. This paper uses pencil theory to provide a structural basis for determining the available degree of flexibility in choosing coefficients of the closed-loop characteristic equation of an output feedback system. Previous results are verified. Extensions are introduced to increase the lower bound on placeable poles and indicate under what conditions additional poles can be placed.