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The reducibility of linear second-order time-varying systems with control and observation. (English. Russian original) Zbl 1423.93086

J. Appl. Math. Mech. 76, No. 4, 413-422 (2012); translation from Prikl. Mat. Mekh. 76, No. 4, 574-586 (2012).
Summary: 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.

MSC:

93B17 Transformations
93B05 Controllability
93B07 Observability
93B10 Canonical structure
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