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A Globally Asymptotically Stable Polynomial Vector Field with Rational Coefficients and no Local Polynomial Lyapunov Function (1803.06087v4)
Published 16 Mar 2018 in math.OC, cs.SY, and math.DS
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.