mathcal Synchronization for Fuzzy Markov Jump Chaotic Systems With Piecewise-Constant Transition Probabilities Subject to PDT Switching Rule
This article investigates the nonfragile <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> synchronization issue for a class of discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems. With regard to the T-S fuzzy mode...
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| Published in | IEEE transactions on fuzzy systems Vol. 29; no. 10; pp. 3082 - 3092 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.10.2021
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| Subjects | |
| Online Access | Get full text |
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| Abstract | This article investigates the nonfragile <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> synchronization issue for a class of discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems. With regard to the T-S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results. |
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| AbstractList | This article investigates the nonfragile <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> synchronization issue for a class of discrete-time Takagi-Sugeno (T-S) fuzzy Markov jump systems. With regard to the T-S fuzzy model, a novel processing method based on the matrix transformation is introduced to deal with the double summation inequality containing fuzzy weighting functions, which may be beneficial to obtain conditions with less conservatism. In view of the fact that the uncertainties may occur randomly in the execution of the actuator, a nonfragile controller design scheme is presented by virtue of the Bernoulli distributed white sequence. The main novelty of this article lies in that the transition probabilities of the Markov chain are considered to be piecewise time-varying, and whose variation characteristics are described by the persistent dwell-time switching regularity. Then, based on the Lyapunov stability theory, it is concluded that the resulting synchronization error system is mean-square exponentially stable with a prescribed <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> performance in the presence of actuator gain variations. Finally, an illustrative example about Lorenz chaotic systems is provided to show the effectiveness of the established results. |
| Author | Xia, Jianwei Shen, Hao Park, Ju H. Wang, Jing Xing, Mengping |
| Author_xml | – sequence: 1 givenname: Jing orcidid: 0000-0002-5519-9016 surname: Wang fullname: Wang, Jing email: jingwang08@126.com organization: School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China – sequence: 2 givenname: Jianwei orcidid: 0000-0002-5330-9349 surname: Xia fullname: Xia, Jianwei email: njustxjw@126.com organization: School of Mathematical Sciences, Liaocheng University, Liaocheng, China – sequence: 3 givenname: Hao orcidid: 0000-0001-7024-6573 surname: Shen fullname: Shen, Hao email: haoshen10@gmail.com organization: School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China – sequence: 4 givenname: Mengping orcidid: 0000-0002-4102-8494 surname: Xing fullname: Xing, Mengping email: 13856079203@163.com organization: School of Electrical and Information Engineering, Anhui University of Technology, Ma'anshan, China – sequence: 5 givenname: Ju H. orcidid: 0000-0002-0218-2333 surname: Park fullname: Park, Ju H. email: jessie@ynu.ac.kr organization: Department of Electrical Engineering, Yeungnam University, Kyongsan, Korea |
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| Snippet | This article investigates the nonfragile <inline-formula><tex-math notation="LaTeX">\mathcal {H}_{\infty }</tex-math></inline-formula> synchronization issue... |
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| SubjectTerms | Actuators Lyapunov methods Markov processes Mean-square exponential stability nonfragile <inline-formula 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"> <tex-math notation="LaTeX"> mathcal{H}_{\infty}</tex-math> </inline-formula> synchronization persistent dwell-time (PDT) switching Switches Synchronization Takagi–Sugeno (T–S) fuzzy Markov jump chaotic systems (TFMJCSs) Uncertainty |
| Title | mathcal Synchronization for Fuzzy Markov Jump Chaotic Systems With Piecewise-Constant Transition Probabilities Subject to PDT Switching Rule |
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| Volume | 29 |
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