Investigation on Synchronization of Two Identical Class of Chaotic Systems Using Back-Stepping Control Technique in the Presence of Time Delays

Time delay analysis is very crucial when it comes to the synchronization of chaotic systems. All practical dynamical systems are described by differential equations, hence the presence of time delay in dynamics becomes a pivotal part of the system analysis. So, in this article, an attempt has been made to study the synchronization problem of two identical same-ordered time-delayed chaotic systems, in strict-feedback form as described in (2) and (3) in master and slave configuration. Unlike other conventional nonlinear control techniques, the back-stepping control design strategy is used to serve the purpose of synchronization. The main advantage of using the back-stepping control technique is that it utilizes only a single scalar controller to attain synchronization among different chaotic systems. A generalized control function
$u\in R$
is designed for the same. For verification of the theoretical results, the 3D time-delayed Genesio-Tesi chaotic system is considered both a master and slave system. Simulation results are provided to support the proposition.