Abstract: This paper focuses on the stabilization problem for time-delay rectangular descriptor systems. To begin with, time-delay dynamic compensator is introduced for feedback compensator, a suitable Lyapunov-krasovskii functional is constructed and advanced integral inequalities are used to deal with the integral terms of functional derivatives, furthermore new stabilization condition for time-delay rectangular descriptor systems is obtained in terms of strict linear matrix inequality (LMI). Based on this stabilization condition, utilizing iterative linear matrix inequality algorithm, the relevant parameter matrices of dynamic compensator and feedback gains are computed. Finally, numerical example is given to demonstrate the advantage and effectiveness of the proposed method in this paper.

Key words: Rectangular descriptor systems, time delay, dynamic compensation, stabilization

摘要： 为研究时滞矩形广义系统的镇定问题，首先引入时滞动态补偿器对系统进行反馈补偿，然后构建一个合适的Lyapunov-Krasovskii泛函，并选取先进的积分不等式来处理泛函导数的积分项，进而获得了以严格线性矩阵不等式(LMI)表示的时滞矩形广义系统的镇定条件。在此基础上，利用迭代线性矩阵不等式的算法计算动态补偿器和反馈增益的参数矩阵。最后，通过数值算例验证了方法的有效性和优越性。

关键词: 矩形广义系统, 时滞, 动态补偿, 镇定