Using the notions of (J, J’)-lossless conjugations and (J, J’)-lossless factorizations, the one and two-block linear time-varying infinite horizon standard H-infinity control problem is solved by means of the chain scattering formalism in this paper. The solutions are shown to exist in the form of non-negative definite Lyapunov stabilizing solutions to two matrix differential Riccati equations and satisfying a spectral radius coupling condition. In addition, a state-space proof of the crucial time-varying J-lossless embedding theorem in H-infinity is also shown by exploiting the cascading structure of the chain scattering formalism and with the standard assumptions on the plant, a proof of necessity of (J, J’)-lossless factorization is also given for the solvability of the H-infinity control problem.