Linear dynamically varying H(infinity) controllers are developed for tracking natural trajectories of a broad class of nonlinear systems defined over compact sets. It is shown that the existence of a suboptimal H(infinity) controller is related to the existence of a bounded solution to a functional algebraic Riccati equation. Even though nonlinear systems running over compact sets could exhibit sensitive dependence on initial conditions, the Riccati solution is continuous in the suboptimal case, but it may be discontinuous in the optimal case.