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Continuity of Thresholded Mode-Switched ODEs and Digital Circuit Delay Models

Authors:

Arman Ferdowsi,

Matthias Függer,

Thomas Nowak,

Ulrich SchmidAuthors Info & Claims

HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

Article No.: 10, Pages 1 - 11

https://doi.org/10.1145/3575870.3587125

Published: 09 May 2023 Publication History

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Abstract

Thresholded mode-switched ODEs are restricted dynamical systems that switch ODEs depending on digital input signals only, and produce a digital output signal by thresholding some internal signal. Such systems arise in recent digital circuit delay models, where the analog signals within a gate are governed by ODEs that change depending on the digital inputs.

We prove the continuity of the mapping from digital input signals to digital output signals for a large class of thresholded mode-switched ODEs. This continuity property is known to be instrumental for ensuring the faithfulness of the model w.r.t. propagating short pulses. We apply our result to several instances of such digital delay models, thereby proving them to be faithful.

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Ferdowsi ASchmid USalzmann J(2023)Accurate Hybrid Delay Models for Dynamic Timing Analysis2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323646(1-9)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323646

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HSCC '23: Proceedings of the 26th ACM International Conference on Hybrid Systems: Computation and Control

May 2023

239 pages

ISBN:9798400700330

DOI:10.1145/3575870

This work is licensed under a Creative Commons Attribution International 4.0 License.

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Association for Computing Machinery

New York, NY, United States

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Published: 09 May 2023

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HSCC '23: 26th ACM International Conference on Hybrid Systems: Computation and Control

May 9 - 12, 2023

TX, San Antonio, USA

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Ferdowsi ASchmid USalzmann J(2023)Accurate Hybrid Delay Models for Dynamic Timing Analysis2023 IEEE/ACM International Conference on Computer Aided Design (ICCAD)10.1109/ICCAD57390.2023.10323646(1-9)Online publication date: 28-Oct-2023
https://doi.org/10.1109/ICCAD57390.2023.10323646

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Continuity and pullback attractors for a non-autonomous reaction-diffusion equation in R N

Singular boundary value problems for ODEs

Discontinuous Galerkin methods for Hamiltonian ODEs and PDEs

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