Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

被引：22

作者：

Ma, Zhengqi ^{[1
,2
]}

Yuan, Shoucheng ^{[1
]}

Meng, Kexin ^{[3
]}

Mei, Shuli ^{[3
]}

机构：

[1] Puer Univ, Sch Math & Stat, Puer 665000, Peoples R China

[2] Hunan Univ Sci & Technol, Sch Math & Computat Sci, Xiangtan 411201, Peoples R China

[3] China Agr Univ, Coll Informat & Elect Engn, Beijing 100083, Peoples R China

来源：

MATHEMATICS | 2023年 / 11卷 / 10期

基金：

中国国家自然科学基金;

关键词：

mean-square stability; stochastic system; G-Brownian motion; Lyapunov-Krasovskii function; linear matrix inequality (LMI); H-INFINITY CONTROL; ROBUST STABILITY; EXPONENTIAL STABILITY; EQUATIONS DRIVEN; STABILIZATION;

D O I：

10.3390/math11102405

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov-Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

引用

页数：16

共 41 条

[1]

Chen W, 2011, TIME CONSISTENT G EX

[2]

Chen Yun, 2009, Acta Automatica Sinica, V35, P324, DOI 10.3724/SP.J.1004.2009.00324

[3] Stability equivalence between the stochastic differential delay equations driven by G-Brownian motion and the Euler-Maruyama method [J].

Deng, Shounian ;

Fei, Chen ;

Fei, Weiyin ;

Mao, Xuerong .

APPLIED MATHEMATICS LETTERS, 2019, 96 :138-146

[4] STATE-FEEDBACK CONTROL OF SYSTEMS WITH MULTIPLICATIVE NOISE VIA LINEAR MATRIX INEQUALITIES [J].

ELGHAOUI, L .

SYSTEMS & CONTROL LETTERS, 1995, 24 (03) :223-228

[5] Delay-dependent Asymptotic Stability of Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion [J].

Fei, Chen ;

Fei, Weiyin ;

Mao, Xuerong ;

Yan, Litan .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 2022, 359 (09) :4366-4392

[6]

Feron E., 1994, LINEAR MATRIX INEQUA, DOI DOI 10.1137/1.9781611970777

[7]

Gahinet P., 1993, P 32 IEEE C DECISION

[8] LMI-based robust H∞ control of uncertain linear jump systems with time-delays [J].

Gao, JP ;

Huang, B ;

Wang, ZD .

AUTOMATICA, 2001, 37 (07) :1141-1146

[9]

Gu K., 2003, CONTROL ENGN SER BIR

[10] Some Improved Razumikhin Stability Criteria for Impulsive Stochastic Delay Differential Systems [J].

Hu, Wei ;

Zhu, Quanxin ;

Karimi, Hamid Reza .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2019, 64 (12) :5207-5213

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