Semi-global stabilisation of a class of non-minimum phase non-linear output-feedback systems

The stabilisation of non-linear systems with unstable zero-dynamics is considered. The non-linear systems are assumed to be transformable to the non-linear output feedback form. The control design starts from the state feedback, and the state variables associated with the zero-dynamics are stabilised first. The state feedback control design is then carried out using backstepping. An observer with linear error dynamics is constructed with a design parameter which can be set at any positive value. The dynamic output feedback control is then designed, by substituting the state in state feedback control with the observed one and imposing a saturation on the control input. The saturation level depends on the domain of the initial state. The proposed control design asymptotically stabilises the system for any prescribed domain of the initial state.