In the framework of asynchronous control, finite-time stabilization and finite-time bounded stabilization of linear time-varying (LTV) switched systems are investigated. A necessary and sufficient condition for finite-time stability (FTS) of LTV switched systems is proposed based on differential matrix inequalities (DMIs). Moreover, we extend the FTS result to the case of finite-time boundedness (FTB), and present a sufficient condition of FTB for LTV switched systems using the average dwell time method which can be used for design proposes. Then we turn to the design problem of asynchronously switched control to guarantee FTS or FTB of LTV switched systems and give a sufficient condition for the state feedback stabilization in the form of nonlinear DMIs (NDMIs). A numerical method is proposed to solve NDMIs approximately. Finally, two examples are given to illustrate the validity of the results.

中文翻译：

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线性时变切换系统的有限时间异步控制

在异步控制框架内，研究了线性时变(LTV)开关系统的有限时间镇定和有限时间有界镇定。基于微分矩阵不等式(DMI)，提出了LTV交换系统有限时间稳定性(FTS)的充要条件。此外，我们将 FTS 结果扩展到有限时间有界 (FTB) 的情况，并使用可用于设计建议的平均驻留时间方法为 LTV 切换系统提供 FTB 的充分条件。然后我们转向异步切换控制的设计问题，以保证 LTV 切换系统的 FTS 或 FTB，并以非线性 DMI（NDMI）的形式给出状态反馈稳定的充分条件。提出了一种近似求解NDMI的数值方法。最后，