Dependence of the Size of the Reachable Set on Parameters in a Second-Order Linear System

The oscillating linear time-invariant system of second order with time-varying bounded control is considered. The reachable set size is studied with respect to bounded parameters of the system. The reachable set size is characterized by a distance from the origin to the most or least distant point of the set in the Euclidean norm. For one case study, the set size is found to be monotonous in all parameters of the system.