Plenty of research achievements on finite-time stability of discrete-time switched systems have been reported; however, there are a few results referred to finite-time unstable subsystems. The design of the average dwell time was not considered alone for finite-time unstable subsystems in the existing literature. The problems of finite-time stability and finite-time boundedness are investigated respectively for a class of discrete-time switched nonlinear systems with partial finite-time unstable modes. By using multiple Lyapunov-like functions, sufficient conditions are derived respectively to ensure that such systems are finite-time stable and finite-time bounded based on an improved mode-dependent average dwell time and iteration technique. Depending on the above results, sufficient conditions, which can guarantee discrete-time switched linear systems finite-time stable and finite-time bounded, are obtained respectively by using matrix inequalities. Finally, numerical examples are given to verify the effectiveness of the proposed methods.

中文翻译：

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一类具有部分有限时间不稳定模态的离散时间切换非线性系统的有限时间稳定性分析

已有大量关于离散时间切换系统有限时间稳定性的研究成果；然而，也有一些关于有限时间不稳定子系统的结果。现有文献中没有单独考虑有限时间不稳定子系统的平均停留时间设计。分别研究了一类具有部分有限时间不稳定模态的离散时间切换非线性系统的有限时间稳定性和有限时间有界问题。通过使用多个类李雅普诺夫函数，基于改进的模式相关平均停留时间和迭代技术，分别导出了充分条件以确保此类系统是有限时间稳定和有限时间有界的。根据以上结果，充分条件，利用矩阵不等式分别得到了保证离散时间切换线性系统有限时间稳定和有限时间有界的问题。最后通过数值算例验证了所提方法的有效性。