Fan, ShuyuanShuyuanFanPan, GuanruGuanruPanWerner, HerbertHerbertWerner2026-08-102026-08-102026-07-29IEEE control systems letters 10: 2149-2154 (2026)https://hdl.handle.net/11420/64323This letter studies prescribed Lyapunov-decay shaping under bounded-input constraints. For a prescribed Lyapunov window, certified decay is evaluated by the corresponding windowed nominal exponential rate. Within the control Lyapunov function framework, the standard linear comparison law is shown to be structurally limited under input bounds, because increasing the exponential rate necessarily increases the required actuation, especially on high Lyapunov levels. Strictly concave comparison laws are then shown to be well suited to this setting: they reduce high-level decay demand while reallocating decay toward lower levels over sufficiently large Lyapunov windows, rather than uniformly increasing the demand over the whole sublevel set. A sufficient feasibility-preserving concave-shaping condition and an endpoint-based design algorithm are developed. Simulations on an inverted pendulum illustrate the theoretical results and the performance of the resulting CLF-QP controllers.en2475-1456202621492154IEEECLF-QPconcave comparison lawControl Lyapunov functiondecay shapinginput saturationTechnology::629: Other Branches::629.8: Control and Feedback Control SystemsTechnology::600: TechnologyJournal Article10.1109/LCSYS.2026.3718009