Analysis and control of a class of uncertain linear periodic discrete-time systems  

作　　者：孙凯 谢广明 

机构地区：[1]LTCS and Center for Systems and Control,College of Engineering, Peking University [2]School of Electrical and Electronics Engineering, East China Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2009年第4期475-488,共14页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China (Nos. 60404001 and60774089)

摘　　要：Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.Feedback control problems for linear periodic systems （LPSs） with interval- type parameter uncertainties are studied in the discrete-time domain. First, the stability analysis and stabilization problems are addressed. Conditions based on the linear matrices inequality （LMI） for the asymptotical stability and state feedback stabilization, respec-tively, are given. Problems of L2-gain analysis and control synthesis are studied. For the L2-gain analysis problem, we obtain an LMI-based condition such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar γ. For the control synthesis problem, we derive an LMI-based condition to build a state feedback controller ensuring that the closed-loop system is asymptotically stable and has an L2-gain smaller than the positive scalar γ. All the conditions are necessary and sufficient.

关 键 词：linear periodic system parameter uncertainty robust stability linear matrix inequality （LMI） state feedback STABILIZATION L2-GAIN 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]