A semi-algebraic view on quadratic constraints for polynomial systems

We show that quadratic constraints admit a semi -algebraic interpretation of dynamic systems. This allows us to improve the analysis of polynomial systems under nonlinear feedback laws by use of the general S -procedure. Extending results to integral quadratic constraints, with the aid of LaSalle's invariance theorem, we obtain a general stability proof for a larger class of multipliers. Numerical results show that the resulting hierarchy of sum -of -squares problems yields much better stability estimates for an exemplary unstable system with nonlinear stabilizing feedback than local approximations. (c) 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY -NC -ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).