Let A(0) be a possibly unbounded positive operator on the Hilbert space H, which is boundedly invertible. Let C(0) be a bounded operator from D(A(0)(1/2)0) (with the norm parallel tozparallel to(1/2)(2) = (A(0)z, z)) to another Hilbert space U. In Part I of this work we have proved that the system of equations <(z)double over dot>( t) + A(0)z(t) + 1/2C(0)*C(0)(z)over dot(t) = C(0)*u(t), y(t) = -C(0)(z)over dot(t) + u(t) determines a well-posed linear system Sigma with input u and output y, input and output space U, and state space X = D(A(0)(1/2)0) x H. Moreover, Sigma is conservative, which means that a certain energy balance equation is satisfied both by the trajectories of Sigma and by those of its dual system. In this paper we show that Sigma is exactly controllable if and only if it is exactly observable, if and only if it is exponentially stable. Moreover, if we denote by A the generator of the contraction semigroup associated with Sigma (which acts on X), then Sigma is exponentially stable if and only if one of the entries in the second column of (iomegaI - A)(-1) is uniformly bounded as a function of omega is an element of R. We also show that, under a mild assumption, Sigma is approximately controllable if and only if it is approximately observable, if and only if it is strongly stable, if and only if the dual system is strongly stable. We prove many related results and we give examples based on wave and beam equations.