Polynomial Constraints for Robustness Analysis of Nonlinear Systems
Year: 2026
Type: preprint
Abstract: This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming, to a broader class of non-polynomial systems. A numerical method for constructing these constraints is proposed. The relationship between polynomial constraints and existing integral quadratic constraints (IQCs) is investigated, providing transformations of IQCs into polynomial constraints. The effectiveness of polynomial constraints in characterizing nonlinearities is validated via numerical examples to compute inner estimates of the region of attraction for two systems.
Source: arXiv (Cornell University)
Authors: Junnarkar, Neelay, Seiler, Peter, Arcak, Murat
Institution: University of Michigan
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7148438779
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