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A Theorem of the Alternative for SOS Lyapunov Functions


H. Peyrl

IEEE Conference on Decision and Control, New Orleans, LA, USA, pp. 1687--1692, Poster

In this paper duality theory is used to derive a theorem of the alternative for the existence of a sums of squares (SOS) Lyapunov function for a system with a polynomial vector field. We show that moments of occupation measures of unstable trajectories are dual feasible solutions providing a natural interpretation of elements in the dual space. We show that moments corresponding to equilibria, orbits, and unbounded solutions indeed provide a certificate of infeasibility of the SOS Lyapunov problem. Additionally, equilibrium points may be recovered from special dual solutions.


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