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arXiv · 2312.03389

Relaxation systems and cyclic monotonicity

Thomas Chaffey·Henk J. van Waarde·Rodolphe Sepulchre
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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.

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Thomas Chaffey, Henk J. van Waarde, Rodolphe Sepulchre. 2023-12-06. Relaxation systems and cyclic monotonicity. https://arxiv.org/abs/2312.03389

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