This page contains a list of preprints, publications, research software, and the PhD thesis.
Preprints
Tripathi, S., & Karabacak, Ö. (2026). Construction of Lyapunov density for nonautonomous dynamical systems on hypertorus. arXiv. [PDF] [DOI] [arXiv]
Gökçen, A., İlhan, F., Şahin, S., Tripathi, S., Kudeyt, M., & Karabacak, Ö. (2026). Dual Lyapunov-based Model Reference Adaptive System Design and Physical VTOL Aircraft Application. [PDF] [DOI] [Preprint]
Tripathi, S., İlhan, F., Gökçen, A., Kudeyt, M., Şahin, S., & Karabacak, Ö. (2026). Construction of Lyapunov Certificates for Oscillatory Systems. Preprints. [PDF] [DOI] [Preprints]
Tripathi, S., & Agarwal, N. (2023). Stability of Reset and Impulsive Continuous-time Linear Switched Systems. arXiv preprint arXiv:2306.10871. [PDF] [DOI] [arXiv]
Publications
Tripathi, S., Kudeyt, M., Gökçen, A., İlhan, F., Şahin, S., & Karabacak, Ö. (2026). Certification of Stability for Systems of Coupled Phase Oscillators. Nonlinear Analysis: Hybrid Systems, Volume 61, 101739. [PDF] [DOI] [SSRN]
Tripathi, S., & Agarwal, N. (2023). Stability of bimodal planar linear switched systems. European Journal of Control, 70, 100767. [PDF] [DOI] [arXiv]
Tripathi, S., & Agarwal, N. (2022). Stability of bimodal planar switched linear systems with both stable and unstable subsystems. International Journal of Systems Science, 53(15), 3254-3285. [PDF] [DOI] [arXiv]
Conference Papers
Doğan, C., Tripathi, S., Gökçen, A., Kudeyt, M., Şahin, S., & Karabacak, Ö. (2025). Torus Üzerindeki Dinamik Sistemler için Kararlılık Sertifikaları. To appear in the Proceedings of the 26th National Conference on Automatic Control (TOK2025). [PDF]
Tripathi, S., Kudeyt, M., Gökçen, A., Şahin, S., & Karabacak, Ö. (2026). Semidefinite Programming Certificates for Synchronization of Kuramoto Oscillators on Arcs. In: Stavrinides, S.G., Ozer, M. (eds) Chaos and Complex Systems. CCS 2025. Springer Proceedings in Complexity. Springer, Cham. [PDF] [DOI] [Abstract] [arXiv]
Gökçen, A., Şahin, S., Kudeyt, M., Tripathi, S., & Karabacak, Ö. (2026). Dual Lyapunov-based Synchronization Control of Rössler System. In: Stavrinides, S.G., Ozer, M. (eds) Chaos and Complex Systems. CCS 2025. Springer Proceedings in Complexity. Springer, Cham. [PDF] [DOI] [Abstract] [arXiv]
Trigonometric Sum of Squares Solver Suite (SOS-t Solver):
For the construction of Lyapunov density and local Lyapunov function for Systems on the d-Torus.
Trigonometric Sum of Squares Solver on Arcs (arcSOS-t Solver):
For the construction of a local Lyapunov function on arcs for generalized Kuramoto models.
Hybrid Sum of Squares Solver-Vectorized (vSOS-hybrid Solver):
For the construction of Lyapunov density and local Lyapunov function for systems with real and angular variables.
Nonautonomous Lyapunov Density on Torus solver (NautLDT-Solver):
A program based on CVX in MATLAB to construct Lyapunov Density for Nonautonomous systems on hypertorus.
*The programs provided here were developed as research implementations for computing Lyapunov densities in a variety of dynamical-system settings. They are intended to accompany the associated research results and may not yet be optimized for software quality or user-friendliness. An eventual long-term objective, through collaborations, could be to consolidate the current implementations into a unified package.
Nikita Agarwal (doctoral supervisor)
Özkan Karabacak (postdoctoral supervisor)