Construction of Lyapunov Certificates for Partial Stability Problems Using Sum of Squares Techniques

A methodology is proposed that allows for algorithmic construction of Lyapunov functions for problems concerning the stability of an equilibrium with respect to part of the variables. This methodology utilizes the previously developed sum of squares technique to determine Lyapunov certificates. Conditions for stability with respect to part of the variables are developed that allow for Lyapunov functions to be determined in terms of a sum of squares. Some examples are presented that highlight these new conditions.