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For pt.I, see ibid., vol.1, no.03CH37475, p.833-8 (2003). This paper contains the second part of the whole investigation on the subject outlined in the paper name. Further we'll use notation and results introduced and presented in the first part. The system under consideration has feedback. So, it is necessary to define exactly main concepts and to prove basic results about the stability of closed-loop systems. This was done in section 7. The H∞ control problem is explicitly stated in section 8. The important preliminary result is stated in section 9. In section 10 the problem is solved for the full-information case (i.e. if y=col(x, w)). The necessary system transformations are justified in section 11. The results on parametrization of the entire set of admissible controllers which solve the problem in special case are collected in section 12. Finally, the main result is stated in section 13. We omit all proofs due to the lack of space.