Robust peak-to-peak gain analysis using integral quadratic constraints

TL;DR

This paper introduces a new framework using integral quadratic constraints to compute upper bounds on the robust peak-to-peak gain of uncertain discrete-time linear systems, aiding safety and reachability analysis.

Contribution

It presents a unified, generalized approach with $ ho$-hard IQCs and terminal costs, improving upon existing methods for robust gain analysis under uncertainty.

Findings

Provides a new IQC-based method for robust peak-to-peak gain bounds.

Demonstrates significant improvements over state-of-the-art techniques.

Validates approach with a numerical example showing enhanced performance.

Abstract

This work provides a framework to compute an upper bound on the robust peak-to-peak gain of discrete-time uncertain linear systems using integral quadratic constraints (IQCs). Such bounds are of particular interest in the computation of reachable sets and the $\ell_1$-norm, as well as when safety-critical constraints need to be satisfied pointwise in time. The use of $\rho$-hard IQCs with a terminal cost enables us to deal with a wide variety of uncertainty classes, for example, we provide $\rho$-hard IQCs with a terminal cost for the class of parametric uncertainties. This approach unifies, generalizes, and significantly improves state-of-the-art methods, which is also demonstrated in a numerical example.