Controlled systems that are robust with respect to initial data

The notion of robustness with respect to initial data is introduced. This means that several control actions map a fixed initial state to the same final state, and the same control actions map any other initial states to the same final one. The following theorem is proved: a controlled system is robust with respect to initial data iff it admits the maximal group of state symmetries. Examples of investigation of specific controlled systems on robustness with respect to initial conditions are presented.