讨论连续~(离散) 时间正线性时滞系统的$L_1(l_1)$-增益性能分析及正控制器设计问题. 由于正系统的非负特性,自然地可利用$L_1(l_1)$- 增益来估计系统的性能. 首先,给出了正线性时滞系统渐近内稳定且满足给定的$L_1(l_1)$-增益指标的充要条件. 然后, 基于上述条件, 针对单输入系统,利用奇异值分解~(SVD) 方法给出了正$L_1(l_1)$- 控制器存在的充要条件,此条件可表示为非线性规划~(NLP) 问题. 并将所给的方法推广到多输入情形,得到了具有特殊形式的$L_1(l_1)$- 控制器的存在条件. 最后,给出数值算例来验证理论结果的有效性.

In this paper, the problems of L1(l1)-gain performance analysis and pos-itive controller design are investigated for continuous-time (discrete-time) positive
linear delay systems. Due to the nonnegative property of positive systems, it is natural to evaluate the system performance via L1(l1)-gain. Firstly, the necessary and sufficient condition is given to guarantee that the positive linear delay system is asymptotically and internally stable and satisfies the prescribed L1(l1)-gain perfor- mance. Then, based on the above condition, for the single-input system, by using the singular value decomposition (SVD) approach, the necessary and sufficient condition is provided for the existence of the positive L1(l1)-controller. This condition can be described as a nonlinear programming (NLP) problem. The proposed approach can be extended to the multi-input case and the existence condition is obtained for the controller with a special form. Finally, two numerical examples are given to show the effeciveness of the theoretical rsults.