Variation of the Size of Reachable Region of Second-Order Linear System

Abstract

A linear time-invariant completely controllable second-order system is considered; all the eigenvalues of this system are different and have negative real parts. The control is considered to be a scalar piecewise continuous function bounded in absolute value. The size of the reachable region is defined as the maximum absolute value of the coordinates of the points of the reachable region on the phase plane. A monotonic dependence of the size of the reachable region on the parameters of the system is shown.