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.

本文讨论了具有部分不稳定模式的非光滑变阶非线性切换系统的全局渐近镇定问题。首先利用Gronwall-Bellman不等式和归纳法验证了所考虑系统解的存在性和唯一性。然后，对稳定模式执行慢速切换策略，并通过快速切换机制处理不稳定模式。在Filippov微分包含的框架下，通过应用依赖于模式的平均驻留时间和驻留时间方案，可以得出足够的稳定标准。最后，介绍了现实生活中的一些物体，并提供了数值模拟，以证明所获得的结果的有效性。