Switching control approach to exponential stabilisation of planar bilinear systems

The authors are interested in the design methodology for a kind of switching control, which, formally, is enough to stabilise the planar bilinear systems. By using a family of parameters to indicate the switching surfaces, the authors bring the qualitative features of subsystems and the geometric property of convex partition into generating and computing a kind of quasi-quadratic Lyapunov function, and then derive the stabilisation conditions. Therefore the switching surfaces can be subject to the stabilisation conditions as well as the optimally arranged conditions. The authors even have some flexibility to improve the dynamical performance, such as excluding sliding motions. They demonstrate the theoretical results with classical examples.