Fixed-Order Controller Design for 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 innerapproximation 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 stabilizing 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 some LMIs. These LMIs can be used for robust pole placement of polytopic systems.