Robust <i>H</i>_<i>∞</i> controller design using frequency‐domain data via convex optimization

Abstract

Summary A new robust controller design method that satisfies the H ∞ criterion is developed for linear time‐invariant single‐input single‐output (SISO) systems. A data‐driven approach is implemented in order to avoid the unmodeled dynamics associated with parametric models. This data‐driven method uses fixed‐order controllers to satisfy the H ∞ criterion in the frequency domain. The necessary and sufficient conditions for the existence of such controllers are presented by a set of convex constraints. These conditions are also extended to systems with frequency‐domain uncertainties in polytopic form. It is shown that the upper bound on the weighted infinity norm of the sensitivity function converges monotonically to the optimal value, when the controller order increases. Additionally, the practical issues involved in computing fixed‐order rational H ∞ controllers in discrete‐time or continuous‐time by convex optimization techniques are addressed. Copyright © 2016 John Wiley &amp; Sons, Ltd.