Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching
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 wi...
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doaj-de712459956b480b90d024057dbd72d02021-03-29T22:00:24ZengIEEEIEEE Access2169-35362019-01-017213852139110.1109/ACCESS.2019.28976148635496Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian SwitchingHaidan Li0Quanxin Zhu1https://orcid.org/0000-0003-3130-4923School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, ChinaMOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, ChinaIn 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.https://ieeexplore.ieee.org/document/8635496/ISFDEsMarkovian switchingdelayed impulse<italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p</italic>th moment exponential stabilityalmost exponential stability |
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DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Haidan Li Quanxin Zhu |
spellingShingle |
Haidan Li Quanxin Zhu Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching IEEE Access ISFDEs Markovian switching delayed impulse <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p</italic>th moment exponential stability almost exponential stability |
author_facet |
Haidan Li Quanxin Zhu |
author_sort |
Haidan Li |
title |
Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching |
title_short |
Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching |
title_full |
Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching |
title_fullStr |
Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching |
title_full_unstemmed |
Stability Analysis of Stochastic Nonlinear Systems With Delayed Impulses and Markovian Switching |
title_sort |
stability analysis of stochastic nonlinear systems with delayed impulses and markovian switching |
publisher |
IEEE |
series |
IEEE Access |
issn |
2169-3536 |
publishDate |
2019-01-01 |
description |
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. |
topic |
ISFDEs Markovian switching delayed impulse <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">p</italic>th moment exponential stability almost exponential stability |
url |
https://ieeexplore.ieee.org/document/8635496/ |
work_keys_str_mv |
AT haidanli stabilityanalysisofstochasticnonlinearsystemswithdelayedimpulsesandmarkovianswitching AT quanxinzhu stabilityanalysisofstochasticnonlinearsystemswithdelayedimpulsesandmarkovianswitching |
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1724192413068558336 |