LMI-Net: Linear Matrix Inequality--Constrained Neural Networks via Differentiable Projection Layers
Linear matrix inequalities (LMIs) have played a central role in certifying stability, robustness, and forward invariance of dynamical systems. Despite rapid development in learning-based methods for control design and certificate synthesis, existing approaches often fail to preserve the hard matrix inequality constraints required for formal guarantees. We propose LMI-Net, an efficient and modular differentiable projection layer that enforces LMI constraints by construction. Our approach lifts the set defined by LMI constraints into the intersection of an affine equality constraint and the positive semidefinite cone, performs the forward pass via Douglas-Rachford splitting, and supports ef...
| Authors | Sunbochen Tang, Andrea Goertzen, Navid Azizan |
|---|---|
| Primary category | cs.LG |
| Published | 7 April 2026 |
| Last updated at source | 7 April 2026 |
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