From time series to dissipativity of linear systems with dynamic supply rates

TL;DR

This paper develops data-driven methods to verify dissipativity of linear systems using quadratic difference forms, providing conditions that are necessary and sufficient for certain supply rates, and linking system identification to dissipativity certification.

Contribution

It introduces a behavioral systems theory approach to assess dissipativity from input-output data, including necessary and sufficient conditions for static supply rates.

Findings

Provided sufficient conditions for data to be informative for dissipativity.

Showed that for static supply rates, data must enable system identification for certification.

Highlighted properties of quadratic difference forms related to storage functions.

Abstract

This paper studies the problem of verifying dissipativity of linear time-invariant (LTI) systems using input-output data. We leverage behavioral systems theory to express dissipativity in terms of quadratic difference forms (QDFs), allowing the study of general dynamic quadratic supply rates. We work under the assumptions that the data-generating system is controllable, and an upper bound is given on its lag. As our main results, we provide sufficient conditions for the data to be informative for dissipativity. We also show that for a specific class of static supply rates, these conditions are both necessary and sufficient. For the latter supply rates, it turns out that certification of dissipativity is only possible from data that enable unique system identification. As auxiliary results, we highlight some properties of QDFs, such as upper bounds on the degree of storage functions.