This article is concerned with the dynamic output‐feedback control problem for continuous‐time switched linear systems with persistent dwell‐time (PDT). Considering the quasi‐periodic property of PDT switching, a discretized quasi‐time‐dependent (QTD) control scheme is proposed by means of a multiple discretized QTD Lyapunov function approach. This control scheme is devoted to designing discretized controllers for continuous‐time switched systems straightforwardly. Firstly, the stability and ‐gain of switched systems with PDT is analyzed utilizing multiple QTD Lyapunov functions. Then, by constructing the quadratic discretized version of these functions, a synthesis condition for the discretized QTD controller is established. In order to formulate the synthesis condition in terms of LMIs, we employ the controller state reset strategy in the derivation, which means that the controller state is reset to that of the plant at each switching instant. Finally, a numerical example is given to illustrate the effectiveness of the proposed control scheme.

中文翻译：

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具有持续停留时间的连续时间线性切换系统的离散准时间控制

本文涉及具有持续停留时间（PDT）的连续时间切换线性系统的动态输出反馈控制问题。考虑到PDT切换的准周期特性，提出了一种采用离散QTD Lyapunov函数方法的离散准时间（QTD）控制方案。该控制方案致力于直接为连续时间切换系统设计离散控制器。首先，利用多个QTD Lyapunov函数分析了带有PDT的交换系统的稳定性和增益。然后，通过构造这些函数的二次离散化形式，为离散化QTD合成条件控制器已建立。为了用LMI表示合成条件，我们在推导中采用了控制器状态重置策略，这意味着在每个切换瞬间，控制器状态都会重置为工厂的状态。最后，给出了一个数值例子来说明所提出的控制方案的有效性。