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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 $y'=f(y,t)+u$, $x,y\in \bbfR\sp{n}$. The authors propose a recursive procedure for designing an appropriate control $u$, which makes the systems synchronized, i.e., $\Vert x(t)-y(t)\Vert \to 0$ 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, coupled oscillators (ODE) 37N35 Dynamical systems in control 34D23 Global stability of ODE 37B25 Lyapunov functions and stability; attractors, repellers 93C10 Nonlinear control systems
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