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

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.