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Mathematics > Optimization and Control

Title: A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function

Abstract: We give an explicit example of a two-dimensional polynomial vector field of degree seven that has rational coefficients, is globally asymptotically stable, but does not admit an analytic Lyapunov function even locally.
Subjects: Optimization and Control (math.OC); Systems and Control (cs.SY); Dynamical Systems (math.DS)
Cite as: arXiv:1803.06087 [math.OC]
  (or arXiv:1803.06087v1 [math.OC] for this version)

Submission history

From: Bachir El Khadir [view email]
[v1] Fri, 16 Mar 2018 06:16:48 GMT (179kb,D)