Simultaneous stabilisation of quadratic input nonlinear systems

In this paper simultaneous stabilisation of a collection of quadratic input nonlinear systems is considered. First, with the help of the technique of control Lyapunov functions (CLFs), a necessary condition, then sufficient conditions for the existence of simultaneously stabilising state feedback controller are derived. Moreover, we present a constructive method for designing continuous simultaneously stabilising controller when the provided sufficient conditions are satisfied. Second, by using the sliding mode technique, this constructive method has been extended to establish a discontinuous control that simultaneously stabilises two levitation systems.