Chaotic systems synchronization. (English) Zbl 1055.34093

Suykens, Johan; Yalçın, Mustak; Vandewalle, Joos

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].

Reviewer: Sergiy Yanchuk (Berlin)

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

Keywords:

synchronization; Lur’e systems; delay; impulsive synchronization