Robust pole assignment via Sylvester equation based state feedback parametrization

Abstract

By using a Sylvester equation based parametrization, the minimum norm robust pole assignment problem for linear time-invariant systems is formulated as an unconstrained minimization problem for a suitably chosen cost function. The derived explicit expression of the gradient of the cost function allows the efficient solution of the minimization problem by using powerful gradient search based minimization techniques. We also discuss how requirements for a particular Jordan structure of the closed-loop state matrix or for partial pole assignment can be accommodated with the proposed approach.