NOVEL DOUBLE INTEGRAL INEQUALITIES AND THEIR APPLICATION TO STABILITY OF DELAYED SYSTEMS

被引：1
|
作者：
Liu, Xinge [1 ]
Xu, Qiaoling [1 ]
Liu, Xiaofan [1 ]
Tang, Meilan [1 ]
Wang, Fengxian [1 ]
机构：
[1] Cent S Univ, Sch Math & Stat, 932 South Lushan Rd, Changsha 410083, Hunan, Peoples R China
来源：
INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL | 2018年 / 14卷 / 05期
基金：
中国国家自然科学基金;
关键词：
Double integral inequality; Time-delay; Stability; Orthogonal approximation; Discontinuous function;
D O I：
10.24507/ijicic.14.05.1805
中图分类号：
TP18 [人工智能理论];
学科分类号：
081104 ; 0812 ; 0835 ; 1405 ;
摘要：
Integral inequalities play an important role in the stability analysis for systems with time-varying delay. In this paper, the orthogonal polynomials of one variable are extended to the orthogonal system of bivariate polynomials. An orthogonal system of bivariate functions which need not be continuous is introduced by triangulating a bounded domain in the plane. The bivariate functions in this orthogonal system need not be polynomials. Based on the orthogonal decomposition of vector and orthogonal approximation of vector, some new double integral inequalities are obtained. These double integral inequalities can provide tighter bounds than most of existing inequalities. Based on these double integral inequalities, an improved sufficient condition on asymptotical stability for systems with time-varying delay is obtained. Several numerical examples are given to show the effectiveness of the stability condition proposed in this paper.
引用
收藏
页码：1805 / 1832
页数：28
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