On a decomposition of multivariable forms via LMI methods

In this paper, it is shown that some of the convenient characteristics of LMI-based methods can be extended to a class of nonlinear systems. The main idea is to use a computationally tractable sufficient condition for positivity of a function, namely the existence of a “sum of squares” representation. By using an extended set of variables and redundant constraints, it is shown that the conditions can be written as linear matrix inequalities in the unknown parameters. To illustrate the method, we present an example dealing with the Lyapunov stability of systems described by polynomial vector fields