Pole Assignment With Static Output Feedback using Algebrogeometric Methods

In this article a solution to the pole assignment problem with output feedback is proposed. Necessary and sufficient conditions are derived which are related to the controllability or observability of the initial system. These arise from the solution of the state-feedback problem using the output or input matrix of the system. For the initial open loop system a new matrix is calculated such that under output feedback the new closed loop system has the desired poles. In the proposed approach, multilineal algebra, algebraic geometry and the theory of generalized inverse matrices are employed. An illustrative example of the proposed method is also given. The main advantage of our approach is that it can be used to derive an algorithm which generates the whole family of output feedback matrices with the required specifications, while avoiding the use of transfer functions.