论文部分内容阅读
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.
The L_1 (l_1) - gain performance analysis and the design of the positive controller for a positive linear time - delay system with continuous (discrete) time are discussed. Due to the nonnegative nature of the positive system, L_1 (l_1) - gain can naturally be used to estimate the system performance Firstly, the necessary and sufficient conditions for the asymptotical internal stability of a positive linear delay system to satisfy a given L_1 (l_1) - gain index are given. Then, The necessary and sufficient conditions for the existence of a positive L_1 (l_1) - controller are given. The condition can be expressed as a nonlinear programming (NLP) problem. The proposed method is generalized to multiple input cases and a special form of L_1 (l_1) - the existence condition of the controller.Finally, a numerical example is given to verify the validity of the theoretical result.