Structured sum of squares for networked systems analysis

In this paper we introduce a structured Sum of Squares technique that enables Sum of Squares programming to be applied to networked systems analysis. By taking the structure of the network into account, we limit the size and number of decision variables in the LMI representation of the Sum of Squares, which improves the scalability of the technique for networked systems beyond taking advantage of symmetry and sparsity. We apply the technique to test non-negativity of fourth order structured polynomials in many variables and show that for these problems the technique has improved scalability over existing Sum of Squares techniques.