Certifying Stability and Performance of Uncertain Differential-Algebraic Systems: A Dissipativity Framework
Abstract
This paper presents a novel framework for characterizing dissipativity of uncertain systems whose dynamics evolve according to differential-algebraic equations. Sufficient conditions for dissipativity (specializing to, e.g., stability or gain bounds) are provided in the case that uncertainties are characterized by integral quadratic constraints. For polynomial or linear dynamics, these conditions can be efficiently verified through sum-of-squares or semidefinite programming. Performance analysis of the IEEE 39-bus power network with a set of potential line failures modeled as an uncertainty set provides an illustrative example that highlights the computational tractability of this approach; conservatism introduced in this example is shown to be quite minimal.
Cite
@article{arxiv.2308.08471,
title = {Certifying Stability and Performance of Uncertain Differential-Algebraic Systems: A Dissipativity Framework},
author = {Emily Jensen and Neelay Junnarkar and Murat Arcak and Xiaofan Wu and Suat Gumussoy},
journal= {arXiv preprint arXiv:2308.08471},
year = {2024}
}