Inferring Global Exponential Stability Properties using Lie-bracket Approximations
<|reference_start|>Inferring Global Exponential Stability Properties using Lie-bracket Approximations: In the present paper, a novel result for inferring uniform global, not semi-global, exponential stability in the sense of Lyapunov with respect to input-affine systems from global uniform exponential stability properties with respect to their associated Lie-bracket systems is shown. The result is applied to adapt dither frequencies to find a sufficiently high gain in adaptive control of linear unknown systems, and a simple numerical example is simulated to support the theoretical findings.<|reference_end|>
@article{weber2024inferring,
    title={Inferring Global Exponential Stability Properties using Lie-bracket
  Approximations},
    author={Marc Weber, Bahman Gharesifard, Christian Ebenbauer},
    journal={arXiv preprint arXiv:2409.03871},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.03871},
    primaryClass={math.OC cs.SY eess.SY}
}