Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling
This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization...
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| Published in: | IEEE transactions on automatic control Vol. 57; no. 10; pp. 2644 - 2650 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
New York, NY
IEEE
01.10.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects: | |
| ISSN: | 0018-9286, 1558-2523 |
| Online Access: | Get full text |
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| Abstract | This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme. |
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| AbstractList | This technical note is concerned with the sampled-data synchronization control problem for a class of dynamical networks. The sampling period considered here is assumed to be time-varying that switches between two different values in a random way with given probability. The addressed synchronization control problem is first formulated as an exponentially mean-square stabilization problem for a new class of dynamical networks that involve both the multiple probabilistic interval delays (MPIDs) and the sector-bounded nonlinearities (SBNs). Then, a novel Lyapunov functional is constructed to obtain sufficient conditions under which the dynamical network is exponentially mean-square stable. Both Gronwall's inequality and Jenson integral inequality are utilized to substantially simplify the derivation of the main results. Subsequently, a set of sampled-data synchronization controllers is designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is employed to show the effectiveness of the proposed sampled-data synchronization control scheme. |
| Author | Zidong Wang Xiaohui Liu Bo Shen |
| Author_xml | – sequence: 1 givenname: Bo surname: Shen fullname: Shen, Bo – sequence: 2 givenname: Zidong surname: Wang fullname: Wang, Zidong – sequence: 3 givenname: Xiaohui surname: Liu fullname: Liu, Xiaohui |
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| Keywords | stochastic sampling Sampled system Probabilistic approach Stabilization Lyapunov method Control synthesis Multiple delay Matrix inequality Exponential stability Synchronization Modeling Gronwall's inequality Dynamical networks sampled-data control Digital control Time varying system Sampling theory Jenson integral inequality synchronization control Efficiency Complex network Integral equation Sampling Lyapunov function |
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| References_xml | – ident: ref15 doi: 10.1109/TSMCB.2009.2022402 – volume: 5 start-page: 51 year: 1986 ident: ref7 article-title: Stochastic sampling in computer graphics publication-title: ACM Trans Graph doi: 10.1145/7529.8927 – ident: ref24 doi: 10.1109/TSMCA.2009.2019875 – ident: ref4 doi: 10.1137/1.9781611970777 – ident: ref3 doi: 10.1080/00207720903045825 – ident: ref11 doi: 10.1109/CDC.2000.914233 – ident: ref13 doi: 10.1109/TSMCB.2009.2024408 – ident: ref6 doi: 10.1109/TCSI.2007.895383 – ident: ref10 doi: 10.1080/00207170903377119 – ident: ref23 doi: 10.1016/j.automatica.2008.07.016 – year: 1997 ident: ref19 publication-title: Stochastic Differential Equations and Their Applications – ident: ref12 doi: 10.1007/s12555-009-0306-5 – volume: 50 start-page: 841 year: 2005 ident: ref17 article-title: A time-varying complex dynamical network model and its controlled synchronization criteria publication-title: IEEE Trans Autom Control doi: 10.1109/TAC.2005.849233 – ident: ref9 doi: 10.1016/j.automatica.2009.03.004 – ident: ref14 doi: 10.1016/j.chaos.2008.04.051 – ident: ref20 doi: 10.1016/j.automatica.2009.05.026 – volume: 46 start-page: 116 year: 2010 ident: ref18 article-title: Global stabilization of complex networks with digraph topologies via a local pinning algorithm publication-title: Automatica doi: 10.1016/j.automatica.2009.10.006 – volume: 38 start-page: 1314 year: 2008 ident: ref16 article-title: Synchronization and state estimation for discrete-time complex networks with distributed delays publication-title: IEEE Trans Syst Man Cybern B doi: 10.1109/TSMCB.2008.925745 – ident: ref22 doi: 10.1109/CDC.1990.203946 – volume: 37 start-page: 418 year: 1992 ident: ref2 article-title: A general framework for linear periodic-systems with applications to <formula formulatype="inline"><tex Notation="TeX">$H_{\infty }$</tex></formula> sampled-data control publication-title: IEEE Trans Autom Control doi: 10.1109/9.126576 – ident: ref25 doi: 10.1109/TCSI.2005.859050 – ident: ref1 doi: 10.1103/RevModPhys.74.47 – ident: ref8 doi: 10.1016/j.sysconle.2004.08.012 – ident: ref5 doi: 10.1007/978-1-4471-3037-6 – ident: ref21 doi: 10.1038/35065725 |
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| SubjectTerms | Applied sciences Computer programs Computer science; control theory; systems Control system synthesis Control systems Control theory. Systems Couplings Detection, estimation, filtering, equalization, prediction Dynamical networks Educational institutions Electronic mail Exact sciences and technology Gronwall's inequality Inequalities Inequality Information, signal and communications theory Jenson integral inequality Linear matrix inequalities Mathematical models Networks Probabilistic logic sampled-data control Sampling Signal and communications theory Signal, noise stochastic sampling Studies Switching theory Synchronism Synchronization synchronization control Telecommunications and information theory |
| Title | Sampled-Data Synchronization Control of Dynamical Networks With Stochastic Sampling |
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