  Certifying the stability of dynamical systems is a central and challenging
task in control theory and systems analysis. To tackle these problems we
present an algorithmic approach to finding polynomial Lyapunov functions. Our
method relies on sums of nonnegative circuit functions (SONC), a certificate of
nonnegativity of real polynomials. We show that both the problem of verifying
as well as the more difficult task of finding Lyapunov functions can be carried
out via relative entropy programming when using SONC certificates. This
approach is analogue yet independent to finding Lyapunov functions via sums of
squares (SOS) certificates and semidefinite programming. Furthermore, we
explore whether using the related, recently introduced DSONC certificate is
advantageous compared to SONC for this type of problem. We implemented our
results, and present examples to show their applicability.
