Lyapunov-level L2-attenuation certificates under input constraints

This letter studies level-dependent L2-attenuation certification for input-constrained nonlinear systems using a given nominal control Lyapunov function as a candidate storage function. A certificate feasibility map is derived that relates the prescribed attenuation bound, the Lyapunov sublevel set, and the minimum input bound needed for feasibility. The map establishes that tightening the attenuation requirement or enlarging the certified sublevel set yields a nondecreasing minimum input requirement. Conversely, under a fixed input limit, the attenuation bound certified by the inverse feasibility map is nondecreasing with the Lyapunov level. This feasibility structure motivates a Lyapunov-level dissipation allocation principle that strengthens dissipation on smaller levels while relaxing it on larger ones. Numerical examples illustrate the level-wise feasibility structure and the performance of the proposed Lyapunov-level dissipation allocation under input saturation.

Subjects

Control Lyapunov functions

disturbance attenuation

input saturation

nonlinear L2-gain

DDC Class

537: Electricity and Electronics

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Lyapunov-level L2-attenuation certificates under input constraints