English

Relaxation systems and cyclic monotonicity

Optimization and Control 2023-12-07 v1

Abstract

It is shown that an LTI system is a relaxation system if and only if its Hankel operator is cyclic monotone. Cyclic monotonicity of the Hankel operator implies the existence of a storage function whose gradient is the Hankel operator. This storage is a function of past inputs alone, is independent of the state space realization, and admits a generalization to nonlinear circuit elements.

Cite

@article{arxiv.2312.03389,
  title  = {Relaxation systems and cyclic monotonicity},
  author = {Thomas Chaffey and Henk J. van Waarde and Rodolphe Sepulchre},
  journal= {arXiv preprint arXiv:2312.03389},
  year   = {2023}
}

Comments

Accepted to the 2023 IEEE Conference on Decision and Control

R2 v1 2026-06-28T13:42:39.269Z