A Data-driven Stability Test for LTI Systems

In this work, we derive a data-based test to assess the stability of discrete-time, linear, time-invariant systems directly from finite datasets of noisy input-output trajectories, without the need to estimate the system matrices or the noise statistics. We characterize the performance of our test and we show that, despite inaccuracies in the data due to the system noise, the test provides accurate results when the available data is sufficiently large yet finite (the required amount of data depends on the properties of the system, which we also characterize). These results complement the body of literature on data-driven control and finite-sample analysis, and they provide new ways to assess the stability of control systems that do not assume, nor require the estimation of, a model of the system and noise and do not rely on solving eigenvalue equations.