Polynomial Constraints for Robustness Analysis of Nonlinear Systems
This work addresses robustness analysis for nonlinear systems, providing a method to extend polynomial tools to non-polynomial cases, but it is incremental as it builds on existing integral quadratic constraints.
The paper tackles the problem of analyzing robustness in nonlinear systems by abstracting non-polynomial components into polynomial constraints, enabling the use of polynomial-based tools like sum-of-squares programming, and validates this with numerical examples to compute inner estimates of the region of attraction for two systems.
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.