The reducibility of linear second-order time-varying systems with control and observation

The possibility of reducing a linear non-autonomous system, containing a control and measurements, to a time-independent form using time-dependent linear transformations of the state, control and observation spaces is investigated. Second-order systems, that is, systems with a second derivative with respect to time, explicitly present in the equations of motion, are examined. The motion of a spacecraft in the neighbourhood of a libration point under the action of a controlling light pressure force is considered as an application, as well as the problem of determining the orientation of an artificial Earth satellite using solar sensing element measurements. In the first problem, controllability and, in the second case, observability is established by reducing the equations to a time-independent form.