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SYNCHRONIZING CONTINUOUS TIME CHAOTIC SYSTEMS OVER NONDETERMINISTIC NETWORKS WITH PACKET DROPOUTS

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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REINALDO M. PALHARES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

Author for correspondence.

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EDUARDO M. A. M. MENDES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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LEONARDO A. B. TORRES

Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos 6627, Belo Horizonte 31270-901, Brazil

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https://doi.org/10.1142/S0218127412503002Cited by:5 (Source: Crossref)

Abstract

The problem of control synthesis for master–slave synchronization of continuous time chaotic systems of Lur'e type using sampled feedback control subject to sampling time random fluctuation and data packet dropouts is investigated. New stability and stabilization conditions are proposed based on Linear Matrix Inequalities (LMIs). The idea is to connect two very efficient approaches to deal with delayed systems: the discretized Lyapunov functional for systems with pointwise delay and the convex analysis for systems with time-varying delay. Simulation examples based on synchronizing coupled Chua's circuits are used to illustrate the effectiveness of the proposed methodology.

Keywords:

References

B. R. Andrievskii and A. L. Fradkov , Autom. Rem. Contr. 65 , 505 ( 2004 ) . Crossref, Web of Science, Google Scholar
J. Cao and D. W. C. Ho , Chaos Solit. Fract. 24 , 1317 ( 2005 ) . Crossref, Web of Science, Google Scholar
H. Dedieu , M. P. Kennedy and M. Hasler , IEEE Trans. Circuits Syst. II: Anal. Digit. Sign. Process. 40 , 634 ( 1993 ) . Crossref, Web of Science, Google Scholar
M. Eisencraft et al. , Commun. Nonlin. Sci. Numer. Simul. 17 , 4707 ( 2012 ) . Crossref, Web of Science, Google Scholar
E. Fridman and M. Dambrine , Automatica 45 , 2258 ( 2009 ) . Crossref, Web of Science, Google Scholar
E. Fridman , M. Dambrine and N. Yeganefar , Automatica 44 , 2364 ( 2008 ) . Crossref, Web of Science, Google Scholar
E. Fridman and G. Tsodik , Eur. J. Contr. 1 , 1 ( 2009 ) . Google Scholar
K. Gu , V. Kharitonov and J. Chen , Stability of Time-Delay Systems ( Birkhäuser , Boston, MA , 2003 ) . Crossref, Google Scholar
J. P. Hespanha , P. Naghshtabrizi and Y. Xu , Proc. IEEE 95 , 138 ( 2007 ) . Crossref, Web of Science, Google Scholar
H. Huang , H.-X. Li and J. Zhong , Int. J. Bifurcation and Chaos 16 , 281 ( 2006 ) . Link, Web of Science, Google Scholar
A. Kruszewski et al. , IEEE Trans. Contr. Syst. Technol. 20 , 887 ( 2012 ) . Crossref, Web of Science, Google Scholar
X. Liao and G. Chen , Int. J. Bifurcation and Chaos 13 , 207 ( 2003 ) . Link, Web of Science, Google Scholar
K. Liu and E. Fridman , Int. J. Robust Nonlin. Contr. 22 , 420 ( 2012 ) . Crossref, Web of Science, Google Scholar
K. Liu and E. Fridman , Automatica 48 , 102 ( 2012 ) . Crossref, Web of Science, Google Scholar
H. Shao , Automatica 45 , 744 ( 2009 ) . Crossref, Web of Science, Google Scholar
F. O. Souza et al. , Int. J. Bifurcation and Chaos 18 , 187 ( 2008 ) . Link, Web of Science, Google Scholar
F. O. Souza et al. , Int. J. Bifurcation and Chaos 18 , 1161 ( 2008 ) . Link, Web of Science, Google Scholar
F. O. Souza , R. M. Palhares and L. A. B. Tôrres , Int. J. Syst. Sci. 42 , 1821 ( 2011 ) . Crossref, Web of Science, Google Scholar
J. Sun , Chaos Solit. Fract. 21 , 143 ( 2004 ) . Crossref, Web of Science, Google Scholar
V. Suplin , E. Fridman and U. Shaked , Automatica 43 , 1072 ( 2007 ) . Crossref, Web of Science, Google Scholar
P. Varutti and R. Findeisen, On the synchronization problem for the stabilization of networked control systems over nondeterministic networks, 2009 American Control Conf. (2009) pp. 2216–2221. Google Scholar
M. E. Yalçin , J. A. K. Suykens and J. Vandewalle , Int. J. Bifurcation and Chaos 11 , 1707 ( 2001 ) . Link, Web of Science, Google Scholar
M. Yu et al. , Eur. J. Contr. 11 , 40 ( 2005 ) . Crossref, Web of Science, Google Scholar
D. Yue , Q.-L. Han and J. Lam , Automatica 41 , 999 ( 2005 ) . Crossref, Web of Science, Google Scholar