Data-Driven Stability and Performance Analysis of Lurye Systems
arXiv:2607.26277
2026
Dynamics
1 ideas extracted · analyzed Aug 31, 2026
What the math gives to ML
The paper provides a constructive data-driven dissipativity certificate for discrete-time Lurye interconnections: an LTI state update in feedback with a memoryless nonlinearity constrained by quadratic inequalities. Its transferable asset is an SDP Lyapunov test that can be built from finite trajectories, including a subspace-identification route when states are unmeasured, rather than requiring an explicit trusted model. The most promising neural-network use is to constrain or monitor recurrent and residual architectures whose activation or feedback block satisfies a known sector or slope bound. This yields a falsifiable stability boundary in terms of the certified contraction matrix and an induced-ell2 gain bound for disturbances or input perturbations.
Ideas from this paper
✓✓ Beats tuned baseline
2026
Represent a recurrent or residual network as a linear state update driven by a memoryless activation or feedback nonlinearity, then solve a data-driven quadratic Lyapunov SDP using excitation trajectories. Accept an update or parameter checkpoint only when the certificate proves contraction and bounds the disturbance-to-output gain. This should prevent exploding hidden states and give a measurable transition between stable and unstable recurrent dynamics.
Useful8/10
Difficulty6/10
Novelty7/10