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Synchronizing chaotic systems using backstepping design. (English) Zbl 1035.34025

The paper deals with the problem of synchronization of coupled systems. Given two systems (possibly exhibiting chaotic dynamics) \(x'=f(x,t)\) and \(y'=f(y,t)+u\), \(x,y\in \mathbb{R}^{n}\). The authors propose a recursive procedure for designing an appropriate control \(u\), which makes the systems synchronized, i.e., \(\| x(t)-y(t)\| \to 0\) as \(t\to\infty\), for some set of initial conditions. The algorithm combines the choice of the Lyapunov function with the design of a controller.

MSC:

34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
37N35 Dynamical systems in control
34D23 Global stability of solutions to ordinary differential equations
37B25 Stability of topological dynamical systems
93C10 Nonlinear systems in control theory
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