{"ID":2837962,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.18374","arxiv_id":"2511.18374","title":"Explicit Bounds on the Hausdorff Distance for Truncated mRPI Sets via Norm-Dependent Contraction Rates","abstract":"We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, fully analytic horizon-selection rule that guarantees a prescribed approximation tolerance without iterative set computations. The choice of vector norm enters as a design lever: norm shaping -- through diagonal or Lyapunov-based weighting -- tightens both the contraction factor and the resulting certificate, with direct consequences for robust invariant-set approximation and tube-based model predictive control (MPC) constraint tightening. Numerical examples illustrate the accuracy, scalability, and practical impact of the proposed bound.","short_abstract":"We derive a computable closed-form upper bound on the Hausdorff distance between a truncated minimal robust positively invariant (mRPI) set and its infinite-horizon limit. The bound depends only on a disturbance-set size measure and an induced-norm contraction factor of the system matrix, and it yields an explicit, ful...","url_abs":"https://arxiv.org/abs/2511.18374","url_pdf":"https://arxiv.org/pdf/2511.18374v2","authors":"[\"Jiaxun Sun\",\"Hengyu Xue\",\"Yuyang Zhao\"]","published":"2025-11-23T09:48:41Z","proceeding":"cs.RO","tasks":"[\"cs.RO\",\"eess.SY\",\"math.DS\"]","methods":"[]","has_code":false}