SOS methods for demonstrating dissipativity for switched systems

Dissipativity is a valuable tool for analysis and synthesis of dynamical systems, however, the search for an appropriate storage function to show the property is often not straightforward. This paper uses sum of squares (SOS) optimization methods to determine whether a nonlinear or switched system is dissipative. This is especially useful for switched systems where notions of dissipativity involve finding multiple storage functions. Examples and relevant software code are provided to illustrate these methods.