{"ID":2840124,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.14626","arxiv_id":"2511.14626","title":"Concave Comparison Functions for Accelerating Constrained Lyapunov Decay","abstract":"What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal exponential rate together with the endpoint cap induced by actuator limits, we establish a strict ordering: concave comparison functions strictly outperform linear and convex ones, and strict concavity is necessary to improve the best achievable global exponential rate under a fixed endpoint cap. We derive a computable lower bound on the required actuation level for a target nominal rate and show that only concave shaping can reduce this level under the endpoint cap. We then establish a feasibility-preserving acceleration result: whenever a margin exists on a sublevel set, a feasible linear comparison can be replaced by a concave one that preserves feasibility while strictly increasing the guaranteed windowed decay. Finally, we give a tunable rational concave factor with controlled slope that yields a constructive design and integrates with CLF QP, as illustrated by examples.","short_abstract":"What limits how fast a Lyapunov function can decay under input bounds? We address this question by showing how the shape of Lyapunov comparison functions governs guaranteed decay for control affine systems. Using a windowed nominal exponential rate together with the endpoint cap induced by actuator limits, we establish...","url_abs":"https://arxiv.org/abs/2511.14626","url_pdf":"https://arxiv.org/pdf/2511.14626v1","authors":"[\"Shuyuan Fan\",\"Guanru Pan\",\"Herbert Werner\"]","published":"2025-11-18T16:16:55Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}