Version 1
: Received: 17 September 2024 / Approved: 18 September 2024 / Online: 18 September 2024 (11:38:06 CEST)
How to cite:
Kudeyt, M.; Tripathi, S.; Gökçen, A.; Şahin, S.; Karabacak, O. Construction of Lyapunov Certificates for Systems on Torus Using Trigonometric Polynomials. Preprints2024, 2024091361. https://doi.org/10.20944/preprints202409.1361.v1
Kudeyt, M.; Tripathi, S.; Gökçen, A.; Şahin, S.; Karabacak, O. Construction of Lyapunov Certificates for Systems on Torus Using Trigonometric Polynomials. Preprints 2024, 2024091361. https://doi.org/10.20944/preprints202409.1361.v1
Kudeyt, M.; Tripathi, S.; Gökçen, A.; Şahin, S.; Karabacak, O. Construction of Lyapunov Certificates for Systems on Torus Using Trigonometric Polynomials. Preprints2024, 2024091361. https://doi.org/10.20944/preprints202409.1361.v1
APA Style
Kudeyt, M., Tripathi, S., Gökçen, A., Şahin, S., & Karabacak, O. (2024). Construction of Lyapunov Certificates for Systems on Torus Using Trigonometric Polynomials. Preprints. https://doi.org/10.20944/preprints202409.1361.v1
Chicago/Turabian Style
Kudeyt, M., Savaş Şahin and Ozkan Karabacak. 2024 "Construction of Lyapunov Certificates for Systems on Torus Using Trigonometric Polynomials" Preprints. https://doi.org/10.20944/preprints202409.1361.v1
Abstract
Amethod for the certification of local and almost global stability of invariant sets of ordinary differential equations on torus is proposed. The method is based on using trigonometric polynomials as candidates of local Lyapunov functions or (global) Lyapunov densities (so-called dual Lyapunov functions) and converting the required local Lyapunov or dual Lyapunov conditions into semidefinite programming. We provide several examples with three and four oscillators to showcase the adaptability of our results, which can be used to certify partial or complete phase-locking/phase-cohesion and to validate the presence of an attracting/repelling set in various scenarios.
Keywords
almost global synchronization; trigonometric polynomials; stability certificates
Subject
Engineering, Control and Systems Engineering
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.