A perturbation method for the solution of the output feedback pole placement problem

In this paper, we will present a simple nondeterminantal constructive method for the output feedback placement problem when mp>n, for a system with p inputs, m outputs and n states. This is a perturbation method and there is no use of any other tools apart from simple matrix algebra. The solution is found by solving a set of linear equations and provides a global linearisation; here, we also give a very elementary and alternative short proof for the existence of solutions to the pole assignment by output feedback when mp>n. This linearisation method is not of the dyadic type, and allows all the degrees of freedom “mp” of the feedback controller to be used