An application of the Sum of Squares Decomposition to the L2gain computation for a class of non linear systems

This paper presents a new approach for determining the L2gain of affine non-linear systems with polynomial vector fields within the sum of squares framework. The main feature of the proposed approach is that it does not require solving a Hamilton Jacobi Inequality (HJI). The solution to the HJI is done indirectly by solving another inequality augmented with slack variables. This new inequality is much easier to solve than the original HJI since it is linear in the Lyapunov function parameters. Numerical examples are given to illustrates the proposed approach.