Introducing some classes of stable systems without any smooth Lyapunov functions

DOI10.1016/j.cnsns.2023.107485zbMath1528.34046OpenAlexW4385638433MaRDI QIDQ6058742

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Publication date: 1 November 2023

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2023.107485

zbMATH Keywords

invariant setslimit cyclesLyapunov stabilitynonlinear dynamical systemssmooth Lyapunov functions

Mathematics Subject Classification ID

Stability of solutions to ordinary differential equations (34D20)

Cites Work

• Review on computational methods for Lyapunov functions
• A weak maximum principle-based approach for input-to-state stability analysis of nonlinear parabolic PDEs with boundary disturbances
• Stability theory by Liapunov's direct method
• Asymptotic stability and smooth Lyapunov functions
• Regularity of Liapunov functions for stable systems
• Stability in the continuous case
• A globally asymptotically stable polynomial vector field with rational coefficients and no local polynomial Lyapunov function
• On a new type of stability
• Piecewise structure of Lyapunov functions and densely checked decrease conditions for hybrid systems
• Lyapunov stability theory of nonsmooth systems
• Smoothing Lyapunov functions
• Computation of Lyapunov functions for nonlinear differential equations via a Massera-type construction
• On the stability of motion
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