Multi‐Objective Robust Controller Synthesis With Integral Quadratic Constraints in Discrete‐Time

ABSTRACT This article presents a novel framework for the robust controller synthesis problem in discrete‐time systems using dynamic Integral Quadratic Constraints (IQCs). We present an algorithm to minimize closed‐loop performance measures such as the ‐norm, the energy‐to‐peak gain, the peak‐to‐peak gain, or a multiobjective mix thereof. While IQCs provide a powerful tool for modeling structured uncertainties and nonlinearities, existing synthesis methods are limited to the ‐norm, continuous‐time systems, or special system structures. By minimizing the energy‐to‐peak and peak‐to‐peak gain, the proposed synthesis can be utilized to bound the peak of the output, which is crucial in many applications requiring robust constraint satisfaction, input‐to‐state stability, reachability analysis, or other pointwise‐in‐time bounds. Numerical examples demonstrate the robustness and performance of the controllers synthesized with the proposed algorithm.