Informativity of noisy data for structural properties of linear systems

TL;DR

This paper develops rank-based tests for determining whether noisy data from an unknown linear system can certify certain structural properties, bypassing the need for precise system identification.

Contribution

It introduces a novel framework for testing system properties directly from noisy data using informativity concepts and geometric analysis, applicable to properties like observability and controllability.

Findings

Rank tests for data informativity established

Geometric framework for property analysis developed

Applicable to noisy input-state-output data

Abstract

This paper deals with developing tests for checking whether an unknown system has certain structural properties. The tests that we are aiming at are in terms of noisy input-state-output data obtained from the unknown system. Since, in general, the data do not determine the unknown system uniquely, many systems are compatible with the same set of data. Therefore we can not apply system identification and apply existing, model based, tests. Instead, we will use the concept of informativity, and establish tests for informativity of the given noisy data. We will do this for a range of system properties, among which strong observability and detectability and strong controllability and stabilizability. These informativity tests will be in terms of rank tests on polynomial matrices that can be constructed from the noisy data. We will also set up a geometric framework for informativity analysis. Within that framework we will give geometric tests for informativity for strong observability, observability, and left-invertibilty.