Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching

被引：5

作者：

Li, Haidan ^{[1
,2
]}

Zhu, Quanxin ^{[3
]}

机构：

[1] Qingdao Univ Sci & Technol, Sch Math & Phys, Qingdao 266061, Peoples R China

[2] Nanjing Normal Univ, Inst Finance & Stat, Sch Math Sci, Nanjing 210023, Jiangsu, Peoples R China

[3] Hunan Normal Univ, Sch Math & Stat, MOE LCSM, Changsha 410081, Hunan, Peoples R China

来源：

IEEE ACCESS | 2019年 / 7卷

基金：

中国国家自然科学基金;

关键词：

ISFDEs; Markovian switching; delayed impulse; pth moment exponential stability; almost exponential stability; FUNCTIONAL-DIFFERENTIAL EQUATIONS; MOMENT EXPONENTIAL STABILITY; CRITERIA; JUMP;

D O I：

10.1109/ACCESS.2019.2897614

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper, we are concerned with the stability analysis of stochastic nonlinear systems with delayed impulses and Markovian switching. Different from the previous literature, the impulses in this paper depend on delays and the jumping parameters are described by a continuous-time Markov chain with a finite-state space. Several novel stability criteria are obtained by using a stochastic Lyapunov function method and the Razumikhin technique. To be less conservative, the Razumikhin condition imposed on the coefficient of the estimated upper bound for the Lyapunov function's time-derivative is improved from a constant to a function, which can be either positive or negative. Finally, we use two examples and their simulations to verify the validity of the theory results.

引用

页码：21385 / 21391

页数：7

共 27 条

[1]

[Anonymous], IEEE T SYST MAN CYBE

[2] Global Exponential Stability of Impulsive Neural Networks With Variable Delay: An LMI Approach [J].

Chen, Wu-Hua ;

Zheng, Wei Xing .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS, 2009, 56 (06) :1248-1259

[3] Exponential stability analysis of impulsive stochastic functional differential systems with delayed impulses [J].

Cheng, Pei ;

Deng, Feiqi ;

Yao, Fengqi .

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2014, 19 (06) :2104-2114

[4] Global exponential stability of impulsive stochastic functional differential systems [J].

Cheng, Pei ;

Deng, Feiqi .

STATISTICS & PROBABILITY LETTERS, 2010, 80 (23-24) :1854-1862

[5] Exponential stability for generalized stochastic impulsive functional differential equations with delayed impulses and Markovian switching [J].

Gao, Lijun ;

Wang, Dandan ;

Zong, Guangdeng .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2018, 30 :199-212

[6] Stochastic stability of nonlinear discrete-time Markovian jump systems with time-varying delay and partially unknown transition rates [J].

Hien, L. V. ;

Dzung, N. T. ;

Trinh, H. .

NEUROCOMPUTING, 2016, 175 :450-458

[7] CONTROLLABILITY, STABILIZABILITY, AND CONTINUOUS-TIME MARKOVIAN JUMP LINEAR QUADRATIC CONTROL [J].

JI, YD ;

CHIZECK, HJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1990, 35 (07) :777-788

[8] Exponential stability and instability of impulsive stochastic functional differential equations with Markovian switching [J].

Kao, Yonggui ;

Zhu, Quanxin ;

Qi, Wenhai .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 :795-804

[9]

Krasovskii NM., 1961, Autom Remote Control, V22, P1021

[10] Exponential stability of hybrid stochastic functional differential systems with delayed impulsive effects: average impulsive interval approach [J].

Li, Dianqiang ;

Cheng, Pei ;

He, Shuping .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2017, 40 (11) :4197-4210

← 1 2 3 →