Real analytic control systems

Using a suitable locally convex topology for the space of real analytic vector fields, we give a characterization of real analytic control systems. Among other things, this class of real analytic control systems has the property that, upon substitution of an open-loop control, the resulting time-varying vector field has a flow depending on initial condition in a real analytic manner. To give context to the real analytic case, we also consider the cases of finitely differentiable and smooth control systems.