一类不确定线性周期离散时间系统的分析与控制  

Analysis and Control of a Class of Uncertain Linear Periodic Discrete-Time Systems

作　　者：孙凯[1] 谢广明[1,2] 

机构地区：[1]北京大学工学院系统与控制中心,北京100871 [2]华东交通大学电气与电子工程学院,南昌330013

出　　处：《应用数学和力学》2009年第4期443-456,共14页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(6077408960404001)

摘　　要：讨论具有参数区间不确定性的线性周期离散时间系统的反馈控制问题.首先进行系统的鲁棒稳定性分析和镇定研究,分别给出了基于线性矩阵不等式的系统渐近稳定和状态反馈镇定的条件.接着研究系统的L2-增益分析和控制综合问题.对于L2-增益分析问题,得到一个基于线性矩阵不等式的条件,在该条件下,具有参数不确定性的线性周期自治系统渐近稳定,且有小于γ的L2-增益.对于控制综合问题,导出基于线性不等式的条件,由该条件可以得到一个状态反馈器,使得闭环系统渐近稳定,且有小于γ的L2-增益.所有这些条件都是充分必要的.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 were addressed. Conditions based on linear matrices inequality for asymptotical stability and state feedback stabilization respectively were given. Problems of L2-gain analysis and control synthesis problems were studied. For the L2- gain analysis problem, an LMI-based condition was obtained such that the autonomous uncertain LPS is asymptotically stable and has an L2-gain smaller than a positive scalar gamma. For the control synthesis problem, an LMI-based condition was derived to build a state feedback controller ensuring the closed-loop system is asymptotically stable and Ires an L2- gain smaller than a positive scalar gamma. All the conditions are necessary and sufficient.

关 键 词：线性周期系统 参数不确定性 鲁棒稳定性 线性矩阵不等式 状态反馈 镇定 L2-增益 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] TP273[自动化与计算机技术—控制科学与工程]