Vahedi Noori and Seiler's data-driven method proves Lurye system stability without models

Control engineers often need to certify stability of Lurye systems—an LTI plant in feedback with a static nonlinearity—but traditional methods require a full state-space model. A new paper by Sahel Vahedi Noori and Peter Seiler (University of Michigan) introduces a fully data-driven framework that replaces the model with trajectory measurements. The first proposed condition directly uses finite input, output, and state trajectories from the nominal LTI block, while the second goes further by reconstructing the state sequence (up to a similarity transformation) from input/output data using deterministic subspace identification. Both conditions are cast as convex semidefinite programs (SDPs), making them computationally tractable.

Under sufficiently exciting inputs and in the absence of noise, the data-driven SDPs recover the exact same induced-ℓ2 gain bound as the classical model-based approach. The authors demonstrate the method on a simple example with a sector-bounded nonlinearity, achieving identical performance guarantees. This work paves the way for certifying nonlinear feedback systems using only experimental data, which is especially valuable when plant models are unknown or too complex to derive analytically.