doi:10.1109/TAC.2025.3540423engSebastián, EduardoAldana-López, RodrigoAragüés, RosarioMontijano, EduardoSagüés, CarlosDistributed Discrete-Time Dynamic Outer Approximation of the Intersection of EllipsoidsART-2025-143141This paper presents the first discrete-time distributed algorithm to track the tightest ellipsoids that outer approximates the global dynamic intersection of ellipsoids. Given an undirected network, we consider a setup where each node measures an ellipsoid, defined as a time-varying positive semidefinite matrix. The goal is to devise a distributed algorithm to track the tightest outer approximation of the intersection of all the ellipsoids. The solution is based on a novel distributed reformulation of the original centralized semi-definite outer Löwner-John program, characterized by a non-separable objective function and global constraints. We prove finite-time convergence to the global minima of the centralized problem in the static case and finite-time bounded tracking error in the dynamic case. Moreover, we prove boundedness of estimation in the tracking of the global optimum and robustness in the estimation against time-varying inputs. We illustrate the properties of the algorithm with different simulated examples, including a distributed estimation showcase where our proposal is integrated into a distributed Kalman filter to surpass the state-of-the-art in mean square error performance.2025http://zaguan.unizar.es/record/15147810.1109/TAC.2025.3540423http://zaguan.unizar.es/record/151478oai:zaguan.unizar.es:151478IEEE TRANSACTIONS ON AUTOMATIC CONTROL (2025), [8 pp.]byhttps://creativecommons.org/licenses/by/4.0/deed.esinfo:eu-repo/semantics/openAccess