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 multi-objective 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.
Cite
@article{arxiv.2503.22429,
title = {Multi-objective robust controller synthesis with integral quadratic constraints in discrete-time},
author = {Lukas Schwenkel and Johannes Köhler and Matthias A. Müller and Carsten W. Scherer and Frank Allgöwer},
journal= {arXiv preprint arXiv:2503.22429},
year = {2025}
}