Input-Output-Data-Enhanced Robust Analysis via Lifting

TL;DR

This paper introduces a data-driven robust analysis method for uncertain linear systems using lifting and data-dependent multipliers, allowing stability and performance guarantees based on noisy input-output data.

Contribution

It presents a novel approach that integrates physical knowledge with data-driven analysis through lifting and linear fractional representations, improving robustness testing.

Findings

Guarantees stability and performance for systems consistent with observed data.

Incorporates prior physical knowledge into data-driven robust analysis.

Uses linear matrix inequalities for computationally tractable testing.

Abstract

Starting from a linear fractional representation of a linear system affected by constant parametric uncertainties, we demonstrate how to enhance standard robust analysis tests by taking available (noisy) input-output data of the uncertain system into account. Our approach relies on lifting the system and the construction of data-dependent multipliers. It leads to a test in terms of linear matrix inequalities which guarantees stability and performance for all systems compatible with the observed data if it is in the affirmative. In contrast to many other data-based approaches, prior physical or structural knowledge about the system can be incorporated at the outset by exploiting the power of linear fractional representations.