Jongeneel, WouterSutter, TobiasKuhn, Daniel2021-06-052021-06-052021-06-05202310.1109/TAC.2022.3213770https://infoscience.epfl.ch/handle/20.500.14299/178687We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and that it simply amounts to shifting the initial matrix by an optimal linear quadratic feedback gain, which can be computed exactly and highly efficiently by solving a standard linear quadratic regulator problem. The proposed approach allows us to learn the system matrix of a stable linear dynamical system from a single trajectory of correlated state observations. The resulting estimator is guaranteed to be stable and offers explicit statistical bounds on the estimation error.Linear dynamical systemsLarge deviations theorySystem identificationStabilitytext::journal::journal article::research article