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