In this second part of this paper, we discuss several important special cases of the problem solved in Part I. These are: disturbance attenuation and passivation, the full information case, the filtering problem, and the case that the to-be-controlled plant is given in input-state-output representation. An interesting aspect is the notion of full information, which we define in terms of the observability of the to-be-controlled variables from the control variables. When the system is given in state space form, we obtain conditions for the existence of a controller that renders a system dissipative in terms of two coupled algebraic Riccati inequalities. The controller turns out to be a feedback system with a transfer function that is proper, but, in general, not strictly proper. Another issue that we study in this paper is feedback implementability. We find conditions under which, in the context of synthesis of dissipative systems, a controlled behavior can implemented by a feedback controller.