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针对一类具有脉冲现象的非线性切换系统,提出了一种基于有限时间稳定lyapunov函数技术和多Lyapunov函数技术相结合的有限时间稳定性分析方法。该方法首先将非线性系统的有限时间稳定性的概念推广到所考虑的脉冲切换系统。然后,利用有限时间Lyapunov函数技术,确保各个子系统达到有限时间稳定。进一步,给出一个有限时间稳定的非线性比较系统。通过多Lyapunov函数技术,保证原系统的Lyapunov函数值不超过比较系统的状态值,由此得到原脉冲非线性切换系统有限时间稳定的充分条件。最后,一个数值例子说明文中方法的有效性。本文所得的研究结果能应用于生产线控制,交通管理,网络控制等实际系统。
Aiming at a class of nonlinear switching systems with impulsive phenomena, a finite-time stability analysis method based on finite-time stable lyapunov functions and multi-Lyapunov functions is proposed. The method first extends the concept of finite-time stability of nonlinear systems to the considered pulse switching system. Then, the finite-time Lyapunov function technique is used to ensure that each subsystem achieves a finite time stability. Further, a finite time stable nonlinear comparison system is given. The multi-Lyapunov function technique is used to ensure that the original system Lyapunov function value does not exceed the system state value, and the sufficient conditions for the finite-time stability of the original nonlinear pulse-switched system are obtained. Finally, a numerical example illustrates the effectiveness of the method in this paper. The results obtained in this paper can be applied to practical systems such as production line control, traffic management and network control.