Finding surface Lyapunov functions through sum-of-squares programming

This work presents a sum-of-squares method to construct polynomial surface Lyapunov functions (SuLF) of arbitrary order for the impact maps of limit cycles in piecewise linear systems (PLS). This work extends previous results on stability analysis of such limit cycles, which utilized quadratic SuLFs. This paper also discusses an initial study of hierarchical jump linear systems where the switching is driven by feedback of low-level dynamical system states and a Markovian process.