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H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information.

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Titel: H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information.
Autoren: Shen, Hao, Xing, Mengping, Xu, Shengyuan, Basin, Michael V., Park, Ju H.
Quelle: IEEE Transactions on Circuits & Systems. Part I: Regular Papers; Feb2021, Vol. 68 Issue 2, p818-828, 11p
Schlagwörter: STATISTICS, EXPONENTIAL stability, LYAPUNOV stability, STABILITY theory, LYAPUNOV functions, MARKOVIAN jump linear systems
Abstract: In this paper, the $\mathcal {H}_{\infty }$ stabilization problem is studied for discrete-time semi-Markov jump singularly perturbed systems (SMJSPSs) with repeated scalar nonlinearities. As the exact statistical information of the sojourn time or the mode transition is difficult to obtain, the case with only partial semi-Markov kernel information available is considered. Furthermore, introducing an external disturbance or nonlinearity into the analysis of discrete-time semi-Markov jump systems (DTSMJSs) meets critical obstacles, since the relation between the system state vectors at two nonadjacent instants is difficult to determine. To address this issue, the variation trend of the Lyapunov function for a semi-Markov jump sequence is analyzed in detail. Subsequently, criteria of mean-square exponential stability (MSES) for DTSMJSs are established for the first time based on the Lyapunov stability theory. By virtue of the criteria obtained and the cone complementary linearization algorithm, a controller ensuring MSES and $\mathcal {H}_{\infty }$ performance for discrete-time nonlinear SMJSPSs is constructed. Finally, the effectiveness and applicability of the proposed method are validated by simulation examples including an inverted pendulum model. [ABSTRACT FROM AUTHOR]
Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information.
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  Data: <searchLink fieldCode="AR" term="%22Shen%2C+Hao%22">Shen, Hao</searchLink><br /><searchLink fieldCode="AR" term="%22Xing%2C+Mengping%22">Xing, Mengping</searchLink><br /><searchLink fieldCode="AR" term="%22Xu%2C+Shengyuan%22">Xu, Shengyuan</searchLink><br /><searchLink fieldCode="AR" term="%22Basin%2C+Michael+V%2E%22">Basin, Michael V.</searchLink><br /><searchLink fieldCode="AR" term="%22Park%2C+Ju+H%2E%22">Park, Ju H.</searchLink>
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  Data: IEEE Transactions on Circuits & Systems. Part I: Regular Papers; Feb2021, Vol. 68 Issue 2, p818-828, 11p
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  Data: <searchLink fieldCode="DE" term="%22STATISTICS%22">STATISTICS</searchLink><br /><searchLink fieldCode="DE" term="%22EXPONENTIAL+stability%22">EXPONENTIAL stability</searchLink><br /><searchLink fieldCode="DE" term="%22LYAPUNOV+stability%22">LYAPUNOV stability</searchLink><br /><searchLink fieldCode="DE" term="%22STABILITY+theory%22">STABILITY theory</searchLink><br /><searchLink fieldCode="DE" term="%22LYAPUNOV+functions%22">LYAPUNOV functions</searchLink><br /><searchLink fieldCode="DE" term="%22MARKOVIAN+jump+linear+systems%22">MARKOVIAN jump linear systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: In this paper, the $\mathcal {H}_{\infty }$ stabilization problem is studied for discrete-time semi-Markov jump singularly perturbed systems (SMJSPSs) with repeated scalar nonlinearities. As the exact statistical information of the sojourn time or the mode transition is difficult to obtain, the case with only partial semi-Markov kernel information available is considered. Furthermore, introducing an external disturbance or nonlinearity into the analysis of discrete-time semi-Markov jump systems (DTSMJSs) meets critical obstacles, since the relation between the system state vectors at two nonadjacent instants is difficult to determine. To address this issue, the variation trend of the Lyapunov function for a semi-Markov jump sequence is analyzed in detail. Subsequently, criteria of mean-square exponential stability (MSES) for DTSMJSs are established for the first time based on the Lyapunov stability theory. By virtue of the criteria obtained and the cone complementary linearization algorithm, a controller ensuring MSES and $\mathcal {H}_{\infty }$ performance for discrete-time nonlinear SMJSPSs is constructed. Finally, the effectiveness and applicability of the proposed method are validated by simulation examples including an inverted pendulum model. [ABSTRACT FROM AUTHOR]
– Name: Abstract
  Label:
  Group: Ab
  Data: <i>Copyright of IEEE Transactions on Circuits & Systems. Part I: Regular Papers is the property of IEEE and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1109/TCSI.2020.3034897
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      – Code: eng
        Text: English
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      – SubjectFull: STATISTICS
        Type: general
      – SubjectFull: EXPONENTIAL stability
        Type: general
      – SubjectFull: LYAPUNOV stability
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      – SubjectFull: STABILITY theory
        Type: general
      – SubjectFull: LYAPUNOV functions
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      – SubjectFull: MARKOVIAN jump linear systems
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      – TitleFull: H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information.
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              Text: Feb2021
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              Y: 2021
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