Lyapunov-level L2-attenuation certificates under input constraints
Publikationstyp
Journal Article
Date Issued
2026-10-06
Sprache
English
Journal
Volume
10
Start Page
2497
End Page
2502
Citation
IEEE Control Systems Letters 10: 2497-2502 (2026)
Publisher DOI
Scopus ID
Publisher
IEEE
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