A discretization approach to sampled‐data stabilization of networked systems with successive packet losses
This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic s...
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Published in | International journal of robust and nonlinear control Vol. 31; no. 10; pp. 4589 - 4601 |
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Main Authors | , , , , |
Format | Journal Article |
Language | English |
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Bognor Regis
Wiley Subscription Services, Inc
10.07.2021
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ISSN | 1049-8923 1099-1239 |
DOI | 10.1002/rnc.5490 |
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Abstract | This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic system with system matrices subject to stochastic characteristic. In order to deal with the difficulties in the calculations of mathematical expectations of both matrix exponential and integral of matrix exponential function, the upper bound of successive packet losses and packet drop rate are assumed to be known and then the probabilities of the number of successive packet losses taking each value in a bounded set are calculated. Based on this, stability criteria are derived by recurring to the law of total expectation, which guarantee the exponential mean‐square stability of resulting closed‐loop discrete‐time stochastic system with a prescribed H∞ performance. Moreover, a controller design procedure is then proposed. Finally, to verify the analysis results and testify the effectiveness and applicability of the designed algorithm, a numerical simulation example is given. |
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AbstractList | This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic system with system matrices subject to stochastic characteristic. In order to deal with the difficulties in the calculations of mathematical expectations of both matrix exponential and integral of matrix exponential function, the upper bound of successive packet losses and packet drop rate are assumed to be known and then the probabilities of the number of successive packet losses taking each value in a bounded set are calculated. Based on this, stability criteria are derived by recurring to the law of total expectation, which guarantee the exponential mean‐square stability of resulting closed‐loop discrete‐time stochastic system with a prescribed H∞ performance. Moreover, a controller design procedure is then proposed. Finally, to verify the analysis results and testify the effectiveness and applicability of the designed algorithm, a numerical simulation example is given. This article is concerned with the stabilization problem for a class of networked systems subject to successive packet losses. Different from the input delay approach used in some existing literature, the continuous‐time system under consideration is first converted into a discrete‐time stochastic system with system matrices subject to stochastic characteristic. In order to deal with the difficulties in the calculations of mathematical expectations of both matrix exponential and integral of matrix exponential function, the upper bound of successive packet losses and packet drop rate are assumed to be known and then the probabilities of the number of successive packet losses taking each value in a bounded set are calculated. Based on this, stability criteria are derived by recurring to the law of total expectation, which guarantee the exponential mean‐square stability of resulting closed‐loop discrete‐time stochastic system with a prescribed H ∞ performance. Moreover, a controller design procedure is then proposed. Finally, to verify the analysis results and testify the effectiveness and applicability of the designed algorithm, a numerical simulation example is given. |
Author | Hu, Zhipei Zhang, Jin Qiu, Li Deng, Feiqi Fan, Zhun |
Author_xml | – sequence: 1 givenname: Zhipei orcidid: 0000-0001-6494-8608 surname: Hu fullname: Hu, Zhipei organization: Ministry of Education – sequence: 2 givenname: Jin orcidid: 0000-0002-6043-309X surname: Zhang fullname: Zhang, Jin organization: Tel Aviv University – sequence: 3 givenname: Feiqi orcidid: 0000-0002-0257-5647 surname: Deng fullname: Deng, Feiqi email: aufqdeng@scut.edu.cn organization: South China University of Technology – sequence: 4 givenname: Zhun surname: Fan fullname: Fan, Zhun organization: Ministry of Education – sequence: 5 givenname: Li orcidid: 0000-0001-7049-4518 surname: Qiu fullname: Qiu, Li organization: Shenzhen University |
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Cites_doi | 10.1016/j.cja.2013.07.024 10.1109/TCYB.2017.2707178 10.1002/rnc.1278 10.1016/j.jfranklin.2017.12.011 10.1109/TPWRS.2016.2634122 10.1016/j.automatica.2019.108684 10.1016/j.automatica.2019.05.064 10.1080/00207179.2012.720034 10.1007/s11432-019-2714-7 10.1016/j.automatica.2015.10.005 10.1109/TAC.2012.2193707 10.1109/TCYB.2019.2894294 10.1016/j.automatica.2009.03.004 10.1109/MNET.2006.1637931 10.1109/TAC.2017.2676986 10.1002/rnc.1607 10.1109/TNNLS.2018.2885873 10.1109/TAC.1976.1101300 10.1002/rnc.3343 10.1016/j.fss.2016.03.011 10.1109/JAS.2019.1911651 10.1080/00207179.2014.896476 10.1109/TNNLS.2021.3051052 10.1002/rnc.4077 10.1002/rnc.5002 10.1109/TSMC.2018.2882590 10.1002/rnc.3559 10.1109/TMECH.2019.2939416 10.1109/TSMC.2019.2930473 |
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Notes | Funding information National Natural Science Foundation of China, 61733008; 61873099; 61873170; 62003204; 62073144; U1813225; Shantou University Scientific Research Foundation for Talents, NTF19031; Natural Science Foundation of Guangdong Province, 2020A1515010441; Science and Technology Development Foundation of the Shenzhen Government, JCYJ20190808144607400; Guangzhou Science and Technology Planning Project, 202002030158; 202002030389 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
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References | 2017; 62 2009; 45 1976; 21 2019; 7 2018; 28 2013; 26 2019; 50 2019; 30 2017; 47 2020; 63 2017; 27 2008; 18 2013; 86 2016; 32 2019; 107 2012; 57 2021; 51 2014; 87 2017; 306 2006; 20 2020; 30 2021 2019; 24 2018; 355 2019 2016; 63 2011; 21 2020; 113 2016; 26 e_1_2_9_30_1 e_1_2_9_11_1 e_1_2_9_10_1 e_1_2_9_13_1 e_1_2_9_12_1 e_1_2_9_15_1 e_1_2_9_14_1 e_1_2_9_17_1 e_1_2_9_16_1 e_1_2_9_19_1 e_1_2_9_18_1 e_1_2_9_20_1 e_1_2_9_22_1 e_1_2_9_21_1 e_1_2_9_24_1 e_1_2_9_23_1 e_1_2_9_8_1 e_1_2_9_7_1 e_1_2_9_6_1 e_1_2_9_5_1 e_1_2_9_4_1 e_1_2_9_3_1 e_1_2_9_2_1 e_1_2_9_9_1 e_1_2_9_26_1 e_1_2_9_25_1 e_1_2_9_28_1 e_1_2_9_27_1 e_1_2_9_29_1 |
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SubjectTerms | Algorithms Control systems design discretization approach Exponential functions H-infinity control Mathematical analysis networked sampled‐data systems Stability criteria Stabilization Stochastic systems successive packet losses Upper bounds |
Title | A discretization approach to sampled‐data stabilization of networked systems with successive packet losses |
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