Nonlinear stability via sum of squares programming

In this talk we present a tutorial introduction to sum of squares (SOS) techniques which can be written as semidefinite programs (SDP) or quadratic form in a set of monomials with the corresponding matrix being positive semidefinite. The possibility of reformulating conditions for a polynomial to be a sum of squares as an SDP is very useful, since we can use the SOS property in a control context as a convenient sufficient condition for polynomial nonnegativity.This approach allows one to search over parametrized polynomial or rational Lyapunov functions for systems with dynamic polynomial functions.