This paper proposes a limit Φ-dependent average dwell time containing the slow and fast limit Φ-dependent average dwell time that are applied to stable and unstable subsystems, respectively. By integrating the new strategy with multiple discontinuous Lyapunov function approach, one gets some stability results of switched singular systems with stable and unstable subsystems. Those results obtained contain the corresponding ones based on average dwell time, limiting average dwell time and mode-dependent average dwell time. Finally, a numerical example is presented to verify the effectiveness of the proposed conclusions.

中文翻译：

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基于极限Φ相关平均停留时间策略的开关奇异系统的稳定性准则

本文提出了一个与极限Φ有关的平均停留时间，其中分别包含了分别应用于稳定子系统和不稳定子系统的慢和快极限Φ相关的平均停留时间。通过将新策略与多个不连续Lyapunov函数方法集成在一起，可以得到带有稳定子系统和不稳定子系统的开关奇异系统的一些稳定性结果。所获得的结果包含基于平均停留时间，极限平均停留时间和模式相关的平均停留时间的相应结果。最后，通过数值例子验证了所提出结论的有效性。