Synchronization of chaotic systems by linear feedback controller
Consider the coupled differential system \((*) \;dx/dt =f(x) + K(y-z), dy/dt=g(y)\) with \(x,y\in \mathbb{R}^n\), \(f(0)=g(0)=0\), \(K= \text{diag} (k_1 , \dots , k_n)\). Let \(\overline{y} (t)\) be a global solution to \(dy/dt=g(y)\) satisfying \(| \overline{y} (t)| \leq M\) for \( t\geq 0\). Under the assumptions \(f(x) \equiv g(x)\), \(K = kI\) where \(I\) is the \(n\times n\)-identity matrix, the authors derive two conditions each of them guaranteeing \(\lim_{t \rightarrow +\infty} \| x(t)- \overline{y} (t)\|=0\) for any solution \((x(t), \overline{y} (t))\) to \((*)\). They prove a negative result on the synchronizability of \((*)\) in case \(f\neq g\).
scientific article; zbMATH DE number 1286579