Output feedback stabilization via reduced-order observer for uncertain switched nonlinear systems

This paper considers the problem of global output feedback stabilization by virtue of a reduced-order observer for a class of switched nonlinear systems with time-varying control gains under arbitrary switching. Firstly, a set of coordinate transformations is used to introduce a scaling gain. Then, state feedback controllers are designed for the individual subsystems of transformed switched system, and a recursive reduced-order observer is constructed to compensate the unavailable system states. Both the controllers and observer show their robustness to time varying control gains and unknown nonlinearities. Finally, by selecting the scaling gain, we guarantee the negative definiteness of the derivative of a common Lyapunov function constructed in this paper, which implies that the proposed output feedback controllers render the switched nonlinear system globally asymptotic stabile under arbitrary switching. An example is given to show the effectiveness of the proposed method.