About the time-optimal problem for one class of two-dimensional bilinear controlled systems

In the paper one class of bilinear two-dimensional controlled systems is considered. For these systems the bang-bang property of time-optimal control is studied. The bang-bang property is very interesting for applications, because bang-bang controls are very suitable for realization in practice. In the paper some efficient conditions for bang-bang property of time-optimal controls are received. In the capacity as example, it was considered some controlled analog of the L. Richardson model which is well-known in political science.