A Controllability Gramain Shaping with LMI Constraints under Bures--Wasserstein Distance

What the math gives to ML

The paper provides a constructive way to shape how exogenous disturbances propagate through a stable linear dynamical system, rather than merely minimizing output error. Its transferable asset is the Bures–Wasserstein geometry of positive-definite covariance and Gramian matrices combined with semidefinite constraints that suppress selected directions while preserving controllability elsewhere. A promising neural-network use is a structured state-space or recurrent block whose latent disturbance Gramian is explicitly matched to a target covariance and constrained along task-critical directions, yielding stable and anisotropic latent dynamics.