Fixed-/predefined-time stabilization and synchronization of memristor chaotic circuits

Abstract

This investigation discusses the problems of fixed-/predefined-time stabilization and synchronization of memristor chaotic circuits (MCCs). Specially, all of the proposed control schemes are differentiable, namely smooth, which are superior to the previous finite-/fixed-time control techniques, because the discontinuous signum and absolute functions are not contained anymore. Comparing with the traditional fast convergence of chaotic systems, the upper-bound estimation of convergence time in this investigation is not only irrelevant to the initial values of MCCs, but also concise and explicit. Moreover, according to the Lyapunov stability theory, the sufficient criteria are established successively for ensuring the fixed-/predefined-time stabilization and synchronization of MCCs. Finally, the numerical simulations are placed to validate the effectiveness and feasibility of obtained results, in which the comparison is made and the effect of controlling parameters on the convergence speed is further explored.