线性时不变参数多项式系统鲁棒指数稳定性的LMI方法  

A Novel LMI Approach to the Robustly Exponential Stability for Linear Time-Invariant Parameter-Polynomial Systems

作　　者：张鹏[1] 赵克友[1] 

机构地区：[1]青岛大学自动化工程学院,山东青岛266071

出　　处：《青岛大学学报（工程技术版）》2009年第1期25-29,共5页Journal of Qingdao University(Engineering & Technology Edition)

摘　　要：为研究线性时不变参数多项式系统的鲁棒渐近稳定性(RAS)和指数率γ鲁棒渐近稳定性(RASγ),采用参数依赖李亚普诺夫函数法和S-procedure技巧,将所提问题转化为线性矩阵不等式(LMI)的可解性检测。当指数衰减率趋于零时,由RASγ结果可导出相应RAS的结果。数值算例显示结论的正确性和计算有效性。This article investigates the robustly asymptotical stability （RAS） and the robustly asymptotical stability with exponential rate γ （RASγ） for linear time-invariant parameter-polynomialsystems. By adopting the parameter-dependent Lyapunov function method and the S-procedure technique, the article presents a novel approach to transform the problems presented, respectively into the feasibility test of a linear matrix inequality （LMI）. The result of RAS is obtained from the one of RASr as the exponential rate tends to zero. A numerical example shows correctness and calculation validity of the results.

关 键 词：鲁棒渐近稳定性 鲁棒指数稳定性 线性时不变参数多项式系统 参数依赖李亚普诺夫函数 LMI 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程] O231[自动化与计算机技术—控制科学与工程]