A hybrid control design for stabilisation of nonlinear systems from the null controllable region*

The present paper addresses the problem of designing a controller to enable stabilisation from the entire null controllable region (NCR) – the set of states from where stabilisation is possible). A recently developed approach for the numerical construction of the NCR is utilised, and first, the validity of the use of the NCR as a constrained control Lyapunov function (CCLF) is established. The analysis reveals the ability of a CCLF-based control design to drive the system to an equilibrium manifold. The CCLF-based control design is then utilised within a hybrid control framework that guarantees the ability to stabilise to the origin. Simulation results are used to illustrate the implementation of the control design.