Robust stabilisation for a class of uncertain nonlinear systems with output constraint satisfaction via controller switching

In this paper, we study the problem of robust stabilisation for a class of uncertain nonlinear systems with output constraint satisfaction via controller switching. We first consider two controllers: one is the invariance controller designed by backstepping which is responsible for constraint satisfaction but does not necessarily stabilise the system; the other is the controller which is in charge of stabilisation without taking the output constraint into account. We then introduce a switching law which orchestrates switching between the two controllers to achieve robust stabilisation with output constraint provided the switching signal satisfies certain conditions. The gains of the invariance controller depend on where the invariance controller is switched on and how to determine the gains is also obtained. Finally, an example of active magnetic bearing system is given to illustrate the effectiveness of the proposed method.