Synchronization of unified chaotic system based on passive control (Q867875)

The paper studies the following control problem: Find a control function \(u=u(x,y)\) such that two systems \(x'=f(x)\) and \(y'=f(y)+u\), where \(x,y \in \mathbb{R}^3\) are synchronized, i.e. \(\| x(t,x_0)-y(t,y_0)\| \to 0\) for any initial conditions \(x_0 = x(0,x_0)\) and \(y_0=y(0,y_0)\). The function \(f\) is chosen to correspond to the so called unified chaotic system, although chaos is not a matter of the paper.