数学
矩阵多项式
多项式矩阵
基质(化学分析)
多项式的
多项式次数
学位(音乐)
应用数学
有界函数
数学分析
材料科学
复合材料
物理
声学
作者
Xian‐Ming Zhang,Qing‐Long Han,Xiaohua Ge
出处
期刊:Automatica
[Elsevier]
日期:2020-12-23
卷期号:125: 109390-109390
被引量:82
标识
DOI:10.1016/j.automatica.2020.109390
摘要
This paper is concerned with sufficient conditions for a class of matrix-valued polynomial inequalities on closed intervals and their application to H∞ filtering for linear systems with time-varying delays. First, a class of higher degree matrix-valued polynomial inequalities are transformed into the first degree matrix-valued polynomial inequalities by introducing some slack matrices. As a result, a convex property is applied to derive sufficient conditions for a class of higher degree matrix-valued polynomial inequalities on closed intervals. Second, by choosing a Lyapunov–Krasovskii functional with a quadratic matrix-valued polynomial on a time-varying delay, and estimating its time-derivative as a third-degree matrix-valued polynomial on the time-varying delay, the proposed sufficient conditions are utilized to formulate a novel bounded real lemma on the existence of H∞ filters for time-delay systems. Third, some algorithms to filter design are provided and discussed in detail. It is pointed out that, if the filter gain is derived through a generalized inverse matrix method, it may be a fake solution, which is demonstrated through a liquid monopropellant rocket motor with a pressure feeding system.
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