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Chaotic systems synchronization. (English) Zbl 1055.34093
Chen, Guanrong (ed.) et al., Chaos control. Theory and applications. Berlin: Springer (ISBN 3-540-40405-8/pbk). Lect. Notes Control Inf. Sci. 292, 117-135 (2003).
The paper gives an overview on methods for the synchronization of coupled Lur’e systems. An individual Lur’e system is described by the equation $$x'=Ax + B \sigma(Cx)$$, where $$x\in \mathbb R^n$$, $$A$$, $$B$$ and $$C$$ are matrices, the nonlinearity $$\sigma$$ is diagonal and satisfies a sector condition. An example of a Lur’e system is Chua’s circuit. The authors consider three different coupling schemes: master-slave coupling, master-slave coupling with delay, and impulsive control.
The synchronization of master-slave systems is discussed by analysing the global asymptotic stability of the error system. Also, nonlinear $$H_\infty$$-synchronization is explained. Finally, a number of illustrations are given.
For the entire collection see [Zbl 1029.00015].

##### MSC:
 34D05 Asymptotic properties of solutions to ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34D35 Stability of manifolds of solutions to ordinary differential equations 34K35 Control problems for functional-differential equations 34C28 Complex behavior and chaotic systems of ordinary differential equations 34H05 Control problems involving ordinary differential equations 34A37 Ordinary differential equations with impulses