Semiglobal stabilization of a class of nonminimum-phase nonlinear output-feedback systems

This paper deals with stabilization of nonlinear systems with unstable zero-dynamics. The nonlinear systems are assumed able to be transformed to a global normal form, as well as to the form of which the observer error dynamics are linear. The control design starts from the state feedback, and the state variables associated with the zero-dynamics are stabilized first. The state feedback control design is then carried out by 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 stabilize the system for any prescribed domain of the initial state.