Reduced Order Synchronization of Two Non-Identical Special Class of Strict Feedback Systems Via Back-Stepping Control Technique

This work offers a systematic technique to achieve reduced order synchronization (ROS) between two different order general classes of chaotic systems in a master-slave configuration. In this study, the dynamics of the master and slave systems are assumed to follow a special class of strict-feedback form, namely, the generalized triangular feedback form. The main objective is to design a suitable scalar controller using a Lyapunov theory-based back-stepping approach such that the mth order slave system gets synchronized with the nth order master system. Due to the difference in the order of the systems (m<n and m=(n-1)), it is only possible to achieve the synchronization between m numbers of states of the slave systems with (n-1) numbers of states of the master system, respectively. We cannot conclude on the stability of the nth state of the master system as there is no counterpart (state) available in the slave system to be synchronized with. Adding an additional (m+1)th state dynamics along with a nonlinear feedback controller (U1) to the slave system ensures that the nth state of the master system is synchronized with the (m+1)th state dynamics of the slave system. With the suggested technique proposed in this article, complete state-to-state synchronization can be achieved with only two controllers. The analytical results are successfully validated through numerical simulations presented in the end.