On the one-shot data-driven verification of dissipativity of LTI systems with general quadratic supply rate function

TL;DR

This paper introduces a one-shot data-driven method to verify dissipativity of LTI systems using a general quadratic supply-rate function, demonstrated through numerical examples including $\

Contribution

It presents a novel approach for verifying dissipativity directly from data without system identification, applicable to various supply-rate functions.

Findings

Effective verification of dissipativity from limited data

Application to $\\mathcal{L}_2$-gain estimation

Verification of a mass-spring-damper system

Abstract

Based on a one-shot input-output set of data from an LTI system, we present a verification method of dissipativity property based on a general quadratic supply-rate function. We show the applicability of our approach for identifying suitable general quadratic supply-rate function in two numerical examples, one regarding the estimation of $\mathcal{L}_2$-gains and one where we verify the dissipativity of a mass-spring-damper system.