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

Amir Ali Ahmadi (a_a_a***at***princeton.edu)
Bachir El Khadir (bkhadir***at***princeton.edu)

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.

Keywords: Polynomial vector fields, Algorithms for testing asymptotic stability, Polynomial Lyapunov functions, Sum of squares optimization, Nonlinear dynamics

Category 1: Applications -- Science and Engineering (Control Applications )

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Citation: Submitted for publication

Download: [PDF]

Entry Submitted: 03/16/2018
Entry Accepted: 03/16/2018
Entry Last Modified: 08/16/2018

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