Stability Region Analysis Using Polynomial and Composite Polynomial Lyapunov Functions and Sum-of-Squares Programming

We propose using (bilinear) sum-of-squares programming for obtaining inner bounds of RoAs for dynamical systems with polynomial vector fields. We search for polynomial as well as composite Lyapunov functions comprised of pointwise maximums of polynomial functions. Results for several examples from the literature are presented using the proposed methods and the PENBMI solver.