Stabilisation control for planar bilinear systems by using switching law to minimise return ratio

By using piecewise constant control, the authors embed planar bilinear system into switching control model. On the basis of interpreting switching stabilisation mechanism in terms of return ratio, they develop a systematic approach to solve the piecewise constant control from the switching law that minimises return ratio. The existence and construction of stabilisation control in a strong way rely on an invariant that characterises the interrelation of the system matrices.