Initial Application of SONC to Lyapunov Stability of Dynamical Systems

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. We construct an algorithm for our results, and examples computed on its implementation showing its applicability.