Fixed time function combination synchronization of perturbed chaotic systems via adaptive control

Summary The concerns of this article is to investigate the fixed time function combination synchronization (FCS) among three different chaotic systems with disturbances. First, a new stability theorem is presented by virtue of the integral inequality technique and a more accurate upper estimation of the convergence time is given. Next, the fixed time FCS problem is considered for the perturbed chaotic systems in which the scaling functions are generated by the bounded dynamical systems. Besides, the synchronization time is related to the control parameters rather than the initial values. The time upper bound can be calculated out by the simple formula, which is the function of control parameters. Finally, a simulation example is provided to illustrate the correctness of the derived criteria.