Exactness verification of sum-of-squares approximations to robust semidefinite programs with functional variables

Robust semidefinite programs (robust SDPs in short) with functional variables are revisited in this paper. We firstly consider the approximate approach suggested by Jennawasin and Oishi (in Proceedings of the 17th IFAC World Congress, Seoul, Korea, July 2008), and then provide a numerically computable condition to verify when the optimal value of an approximate problem is actually equal to that of the original robust SDP. The idea is based on capturing some special structure of a dual feasible solution of the approximate problem.