On the attainability set for a nonlinear system in the plane (Q1878763)

The paper considers certain properties of the reachable set at a finite time of the plane nonlinear control system \[ \dot x=Ax+u\varphi(x)b, \quad x\in \mathbb{R}^2, \, u_1\leq u\leq u_2, \] with scalar input, where \(a\) and \(b\) are a constant matrix and vector of the corresponding dimension such that the vectors \(b\) and \(Ab\) are linearly independent and \(\varphi\) is a continuously differentiable function satisfying certain conditions. In particular, it is proved that every boundary point of the reachable set of this system can be attained by using a bang-bang control with no more than one switching point.