Global output feedback stabilisation of a class of nonlinear systems with unstable zero dynamics

This paper deals with output feedback stabilisation of a class of nonlinear systems with nonlinearity of the unmeasured state variables. The nonlinearity of the unmeasured state complicates the zero dynamics of the nonlinear system and makes the control design more difficult. In this paper, the zero dynamics analysed for the class of nonlinear systems with respect to the original output and then with respect to a virtual output. It is demonstrated that nonlinear systems with unstable zero dynamics may have stable zero dynamics with the virtual output. Based on the analysis, conditions are then identified for nonlinear systems which can be stabilised by control design with estimated state, including the estimated virtual output, and this removes a restriction of a recent result that requires the transformed system has no zero dynamics. Examples are included to demonstrate that the proposed control design can be used to stabilise nonlinear systems with unstable nonlinear zero dynamics.