Abstract For a practical system with switching actions, it is necessary to restrict the switching frequency under the limit of its physical constraints, avoiding potential damage to the equipment. In this paper, a mixed switching scheme with both state-dependent and time-dependent functions is designed to reduce the switching frequency. First, a constant dwell-time constraint is considered and a switching logic called dwell-time min-switching rule is designed to ensure the asymptotic stability of switched system. Particularly, our result is found to be able to cover some previous results for min-switching strategy. Subsequently, a switching function with ranged dwell time scheme which means the dwell time belongs to a range other than a fixed value is taken into account. Furthermore, L 2 stabilization is studied, and the feedback controller design is incorporated into the framework of dwell-time min-switching logic. Finally, several numerical examples are presented to illustrate our results.

中文翻译：

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连续时间切换线性系统的稳定性：混合切换方案

摘要 对于具有开关动作的实际系统，需要将开关频率限制在其物理约束范围内，避免对设备造成潜在的损坏。在本文中，设计了一种具有状态相关和时间相关功能的混合开关方案来降低开关频率。首先，考虑恒定驻留时间约束，并设计称为驻留时间最小切换规则的切换逻辑以确保切换系统的渐近稳定性。特别是，我们发现我们的结果能够覆盖一些以前的最小切换策略的结果。随后，考虑具有范围驻留时间方案的切换功能，这意味着驻留时间属于非固定值的范围。此外，研究了 L 2 稳定性，并且反馈控制器设计被纳入停留时间最小切换逻辑的框架中。最后，给出了几个数值例子来说明我们的结果。