# Monotone one-port circuits

@article{Chaffey2021MonotoneOC, title={Monotone one-port circuits}, author={Thomas Chaffey and Rodolphe Sepulchre}, journal={ArXiv}, year={2021}, volume={abs/2111.15407} }

—Maximal monotonicity is explored as a gener- alization of the linear theory of passivity, aiming at an algorithmic input/output analysis of physical models. The the- ory is developed for maximal monotone one-port circuits, formed by the series and parallel interconnection of basic elements. These circuits generalize passive LTI transfer functions. Periodic input signals are shown to be mapped to periodic output signals, and these input-output behav-iors can be efﬁciently computed using a…

## 5 Citations

### Circuit Analysis using Monotone+Skew Splitting

- MathematicsArXiv
- 2022

—It is shown that the behavior of an m -port circuit of maximal monotone elements can be expressed as a zero of the sum of a maximal monotone operator containing the circuit elements, and a…

### Port-Hamiltonian systems and monotonicity

- Mathematics
- 2022

. The relationships between port-Hamiltonian systems modeling and the notion of monotonicity are explored. The earlier introduced notion of incrementally port-Hamiltonian systems is extended to…

### Circuit Model Reduction with Scaled Relative Graphs

- Mathematics, Computer Science2022 IEEE 61st Conference on Decision and Control (CDC)
- 2022

The Scaled Relative Graph (SRG) gives a graphical representation of the original and truncated port behaviors which gives a bound on the approximation error, which is shown to be competitive with existing methods.

### Spiking Control Systems

- Computer ScienceProceedings of the IEEE
- 2022

The central thesis is that the mixed nature of spiking results from a mixed feedback principle, and a control theory of mixed feedback can be grounded in the operator theoretic concept of maximal monotonicity.

### Convergence Analyses of Davis-Yin Splitting via Scaled Relative Graphs

- Computer Science
- 2022

This work formalizes an SRG theory for the DYS operator and uses it to obtain tighter contraction factors and to study the linear rates of convergence of operator splitting methods.

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