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LMI criteria for robust chaos synchronization of a class of chaotic systems. (English) Zbl 1131.34038

The subject of the paper is the following coupled system in the master-slave configuration \[ \dot x = (A+A_1(t))x + f(x,t) + d_1(t), \]
\[ \dot y = (A+A_2(t))y + f(x,t) + d_2(t) + BK(y-x), \] where \(x,y \in \mathbb R^n\), \(A\) is a constant \(n\times n\) matrix, \(A_1(t)\) and \(A_2(t)\) are perturbation matrices, \(d_1(t)\) and \(d_2(t)\) are external perturbations, \(K\in \mathbb R^{1\times n}\) is a feedback gain and \(B\in \mathbb R^{n\times 1}\) the coupling matrix.
Using the Lyapunov stability theory, the paper provides sufficient conditions for synchronization, i.e. when \(\| x(t)-y(t)\| \to 0\) as \(t\to \infty\).

MSC:

34D05 Asymptotic properties of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34D10 Perturbations of ordinary differential equations
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References:

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