In this paper, the augmented Lyapunov-Krasovskii function approach combining with singular value decomposition method is developed for stabilization of linear descriptor systems with time-varying delay. The delay function is non-differentiable, but continuous and bounded. By introducing a set of improved Lyapunov-Krasovskii functionals we propose delay-dependent sufficient conditions for admissibility of the system in terms of linear matrix inequalities. Then, based on the obtained stability results the problem of stabilization is solved via state feedback controllers, which guarantees that the descriptor closed-loop system is admissible. An numerical example with simulation is provided to show the effectiveness of the theoretical result.

中文翻译：

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线性描述符时变延迟系统的状态反馈镇定

在本文中，结合奇异值分解方法的增广Lyapunov-Krasovskii 函数方法被开发用于具有时变延迟的线性描述符系统的镇定。延迟函数是不可微的，但连续且有界。通过引入一组改进的 Lyapunov-Krasovskii 泛函，我们根据线性矩阵不等式提出了延迟相关的系统可接受性的充分条件。然后，基于获得的稳定性结果，通过状态反馈控制器解决稳定性问题，保证描述符闭环系统是可接受的。提供了一个带有仿真的数值例子来证明理论结果的有效性。