Change of the Attainability Set after Transition to a Reduced System

An example of a linear completely contrallable time-invariant system is considered to study the change of its attainability region after the transition to a reduced system with a decreased order. The original system is a triple integrator. After reduction, a new system (a double integrator) whose control belongs to the set of piecewise continuous bounded functions is considered. The attainability set of the reduced system and the projection of the attainability set of the original system onto the coordinate plane of the reduced system are compared.