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 in...

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Bibliographic Details
Published inAutomatica (Oxford) Vol. 163; p. 111549
Main Authors Cunis, Torbjørn, Pfifer, Harald
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.05.2024
Subjects
Application of nonlinear analysis and design
Lyapunov methods
Stability of nonlinear systems
Stability of nonlinear systems
Application of nonlinear analysis and design
Lyapunov methods
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ISSN0005-1098
1873-2836
DOI10.1016/j.automatica.2024.111549

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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2024.111549