Bounds for Input- and State-to-Output Properties of Uncertain Linear Systems

TL;DR

This paper develops convex algorithms to compute parametric bounds on input-to-output and state-to-output gains in uncertain linear systems, providing more informative insights into how uncertainties influence system performance.

Contribution

It introduces theoretical results and convex algorithms for deriving parametric bounds on system gains, improving upon traditional worst-case approaches.

Findings

Convex algorithms for parametric bounds

Quantitative analysis of uncertainty effects

Enhanced understanding of system performance under uncertainty

Abstract

We consider the effect of parametric uncertainty on properties of Linear Time Invariant systems. Traditional approaches to this problem determine the worst-case gains of the system over the uncertainty set. Whilst such approaches are computationally tractable, the upper bound obtained is not necessarily informative in terms of assessing the influence of the parameters on the system performance. We present theoretical results that lead to simple, convex algorithms producing parametric bounds on the $\mathcal{L}_2$-induced input-to-output and state-to-output gains as a function of the uncertain parameters. These bounds provide quantitative information about how the uncertainty affects the system.