Robust Pole Placement of Systems with Polytopic Uncertainty Via Convex Optimization

Convex parameterization of fixed-order robust stabilizing controllers for systems with polytopic uncertainty is represented as an LMI using KYP Lemma. This parameterization is a convex inner-approximation of the whole non-convex set of stabilizing controllers and depends on the choice of a central polynomial. It is shown that with an appropriate choice of the central polynomial, the set of all fixed-order controllers that place the closed-loop poles of a polytopic system in a disk centered on the real axis, can be outbounded with an LMI. This way, robust regional pole placement can be achieved by convex optimization for systems with polytopic uncertainty.