Stabilization of non-smooth variable order switched nonlinear systems

Abstract The paper discusses the issue of global asymptotic stabilization for non-smooth variable order nonlinear switched systems with partial unstable modes. The existence and uniqueness of solution for the considered system is firstly verified by utilizing Gronwall–Bellman inequality and the inductive method. Then, a slow switching strategy is performed for the stable modes and the unstable modes are handled by a fast switching mechanism. Under the framework of Filippov differential inclusion, sufficient stabilization criteria are derived by applying the mode-dependent average dwell time and dwell time schemes. Finally, some objects in real life are introduced and a numerical simulation is offered to show the validity of the obtained results.