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arXiv · 1901.05794

Construction of Lyapunov functions using Helmholtz-Hodge decomposition

Tomoharu Suda
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Abstract

The Helmholtz-Hodge decomposition (HHD) is applied to the construction of Lyapunov functions. It is shown that if a stability condition is satisfied, such a decomposition can be chosen so that its potential function is a Lyapunov function. In connection with the Lyapunov function, vector fields with strictly orthogonal HHD are analyzed. It is shown that they are a generalization of gradient vector fields and have similar properties. Finally, to examine the limitations of the proposed method, planar vector fields are analyzed.

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Tomoharu Suda. 2019-01-17. Construction of Lyapunov functions using Helmholtz-Hodge decomposition. https://doi.org/10.3934/dcds.2019103

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