Explicit SOS decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov lemma

The purpose of this paper is twofold. The first is to make explicit the relationship between sum of squares (SOS) decompositions of univariate polynomial matrices and the Kalman-Yakubovich-Popov (KYP) lemma. The second is to present an efficient algorithm for explicitly finding an SOS decomposition of such matrices, inspired by the Hamiltonian-type methods for the solution of Riccati equations.