Adaptive Backstepping Stabilization of Uncertain Switched Nonlinear Systems in Parametric Strict-Feedback Form

This paper considers the stabilization problem for a class of parametric switched nonlinear systems under arbitrary switching and parameter uncertainty. A parametric strict-feedback form is adopted in order to represent the switched system. Using the adaptive backstepping approach a common control Lyapunov function under simultaneous domination assumption is constructed and then a control input is designed such that the system is globally asymptotically stable. The design method is developed in a recursive manner and results in an overparametrized adaptive controller. The procedure is illustrated by a descriptive example and the simulation results verify the effectiveness of the designed controller in the system performance.