Controller Synthesis for Positive Systems Under e1 -induced Performance

作     者：Xiaoming Chen, James Lam, Ping Li Department of Mechanical Engineering, The University of Hong Kong Zhan Shu the Electro-Mechanical Engineering Group, Faculty of Engineering and the Environment, University of Southampton 

会议名称：《第24届中国控制与决策会议》

会议日期：2012年

学科分类：0711[理学-系统科学] 07[理学] 08[工学] 081101[工学-控制理论与控制工程] 0811[工学-控制科学与工程] 071102[理学-系统分析与集成] 081103[工学-系统工程] 

基　　金：partially supported by GRF HKU 7138/10E 

关 键 词：Iterative algorithm Linear Lyapunov func- tions 1 -induced performance Positive systems 

摘      要：In this paper, we investigate the problem of controller design for positive systems with the use of linear Lyapunov function. We first present an analytical method to compute the exact value of the 1 -induced norm. Then, we propose a novel characterization under which discrete positive system is asymptotically stable with a prescribed 1 -induced performance. Based on the characterization, a necessary and sufficient condition for the existence of desired controllers is presented, and an iterative linear matrix inequality approach is developed to solve the design condition. Finally, a numerical example is given to illustrate the effectiveness of the proposed theoretical results.