Almost sure stability of hybrid stochastic systems under asynchronous Markovian switching

被引：23

作者：

Luo, Shixian ^{[1
]}

Deng, Feiqi ^{[1
]}

Zhang, Bo ^{[2
]}

Hu, Zhipei ^{[3
]}

机构：

[1] South China Univ Technol, Sch Automat Sci & Engn, Guangzhou 510640, Guangdong, Peoples R China

[2] Guangdong Univ Technol, Sch Automat, Guangzhou 510006, Guangdong, Peoples R China

[3] Shantou Univ, Sch Elect & Informat Engn, Shantou 515063, Peoples R China

来源：

SYSTEMS & CONTROL LETTERS | 2019年 / 133卷

基金：

中国国家自然科学基金;

关键词：

Hybrid stochastic systems; Asynchronous switching control; Markovian jump; Almost sure stability; JUMP LINEAR-SYSTEMS; DIFFERENTIAL-EQUATIONS; STABILIZATION; DESTABILIZATION; DELAY;

D O I：

10.1016/j.sysconle.2019.104556

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper presents two novel Lyapunov methodologies for almost sure stability of hybrid stochastic systems under asynchronous Markovian switching. One is established by a concave composite Lyapunov function with exponential martingale inequality. The other is derived by the strong law of large numbers, which can explore the coupling between the drift part and diffusion part of the systems, thus fully capturing the stabilizing effect of the stochastic noise. Both of these stability conditions give a quantitative relationship between the size of the detected delay of switching signal, the stationary distribution and the generator of Markov chain. As applications, easy-to-check stability and stabilization criteria are further provided for one-sided growth nonlinear systems and linear systems. Numerical examples illustrate the proposed theoretical results. (C) 2019 Elsevier B.V. All rights reserved.

引用

页数：7

共 33 条

[1] Stabilization and destabilization of nonlinear differential equations by noise
Appleby, John A. D.
Mao, Xuerong
Rodkina, Alexandra
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2008, 53 (03) : 683 - 691
[2] Lyapunov exponents of hybrid stochastic heat equations
Bao, Jianhai
Mao, Xuerong
Yuan, Chenggui
[J]. SYSTEMS & CONTROL LETTERS, 2012, 61 (01) : 165 - 172
[3] Stabilization of hybrid neutral stochastic differential delay equations by delay feedback control
Chen, Weimin
Xu, Shengyuan
Zou, Yun
[J]. SYSTEMS & CONTROL LETTERS, 2016, 88 : 1 - 13
[4] Guaranteed cost control for uncertain Markovian jump systems with mode-dependent time-delays
Chen, WH
Xu, JX
Guan, ZH
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2003, 48 (12) : 2270 - 2277
[5] Output feedback control of Markov jump linear systems in continuous-time
de Farias, DP
Geromel, JC
do Val, JBR
Costa, OLV
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2000, 45 (05) : 944 - 949
[6] Stochastic stabilization of hybrid differential equations
Deng, Feiqi
Luo, Qi
Mao, Xuerong
[J]. AUTOMATICA, 2012, 48 (09) : 2321 - 2328
[7] Almost sure exponential stabilisation of stochastic systems by state-feedback control
Hu, Liangjian
Mao, Xuerong
[J]. AUTOMATICA, 2008, 44 (02) : 465 - 471
[8] Stochastic stabilization and destabilization of nonlinear differential equations
Huang, Lirong
[J]. SYSTEMS & CONTROL LETTERS, 2013, 62 (02) : 163 - 169
[9] On Almost Sure Stability of Hybrid Stochastic Systems With Mode-Dependent Interval Delays
Huang, Lirong
Mao, Xuerong
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 2010, 55 (08) : 1946 - 1952
[10] On Input-to-State Stability of Switched Stochastic Nonlinear Systems Under Extended Asynchronous Switching
Kang, Yu
Zhai, Di-Hua
Liu, Guo-Ping
Zhao, Yun-Bo
[J]. IEEE TRANSACTIONS ON CYBERNETICS, 2016, 46 (05) : 1092 - 1105

← 1 2 3 4 →