# On chaotic observer design

Chapter

## Abstract

Chaos synchronization is an extremely exciting subject within the physics and communications society and deals with the remarkable observation that certain chaotic dynamic systems exhibit asymptotically identical motion under weak coupling between the systems. Mathematically, synchronization of two systems — sometimes called transmitter and receiver—can be cast in the following form. Given the single output system ∑ introduce the system ∑

_{1}on IR^{ n }defined by$$\sum\nolimits_1 {:\left\{ \begin{array}{l}
\dot x = f(x) = f({x_1},{x_2}, \ldots ,{x_n}){x_1}\\
y = h(x) = {x_1}
\end{array} \right.} $$

_{2}as a copy of ∑_{1}with the first state component identical to*y*, that is$$\sum\nolimits_{2} {:\left\{ {\begin{array}{*{20}{c}} {\dot{\tilde{x}} = f({{x}_{1}},{{{\tilde{x}}}_{2}}, \ldots ,{{{\tilde{x}}}_{n}})} \hfill \\ {y = h(\tilde{x}) = {{{\tilde{x}}}_{1}}} \hfill \\ \end{array} } \right.}$$

## Keywords

Chaotic System Slide Mode Control Chaos Synchronization Chaotic Dynamic System Chaotic Nature
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## References

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*Controlling chaos*, Academic Press, London, 1996.MATHGoogle Scholar - [2]H. Nijmeijer and I.M.Y. Mareels, “An observer looks at chaos”, IEEE Trans. Circuits and Systems I, Vol. 44, pp. 882–890, 1997.MathSciNetCrossRefGoogle Scholar
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*On the dynamics of two coupled parametrically driven pendulums*, PhD thesis, University of Twente, 1997.Google Scholar - [4]J. Gauthier, H. Hammouri and S. Othman, “A simple observer for nonlinear systems, applications to bioreactors”, IEEE Trans. Automat. Contr. Vol. 37, pp. 875–880, 1992.MathSciNetMATHCrossRefGoogle Scholar
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© Springer-Verlag London Limited 1999