Robust finite-time global synchronization of chaotic systems with different orders

This article proves that the robust finite-time synchronization behavior can be achieved for the chaotic systems with different orders. Based on the Lyapunov stability theory and using the nonlinear feedback control, sufficient algebraic conditions are derived to compute the linear controller gains. These gains are then used to achieve the robust finite time increasing order and reduced order synchronization of the chaotic systems. This study also discusses the design of a controller that accomplishes the finite time synchronization of two chaotic systems of different dimensions under the effect of both unknown model uncertainties and external disturbances. Numerical simulation results are furnished to validate the theoretical findings.