An algorithmic method for checking global asymptotic stability of nonlinear polynomial systems with parameters

An algorithm is presented here, for checking the global asymptotic stability of polynomial dynamical systems with parametric coefficients. It is based on the possibility of writing the polynomials, as sums of products of first degree polynomials, with artificial parametrical coefficients. By giving to all the parameters certain values, we ensure the positiveness of some quantities, constructing thereby proper Lyapunov functions, which guarantee the stability of the equilibrium point.