Zusammenfassung
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.
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