Choosing wx = 1+x1 ≥ 0, and given that Vx is a polynomial function, the algorithm for finding the Lyapunov function must include −1+x12 /δx f x as SOS inequality to satisfy the second condition of the stability theorem.
Ejemplo 3.2 Khalil, 2002. Encontrar una función polinómica de Lyapunov para mostrar la estabilidad del origen del sistema dado por