Fixed-Time-Synchronized Stability and Stabilization for Chaotic Systems: Based on Norm Normalized Sign Function

This paper investigates fixed-time-synchronized (FTS) stability of dynamical systems and stabilization for chaotic systems, and all state elements must converge to the equilibrium point simultaneously. First, we introduce the concepts of FTS stability and ratio persistence. On this basis, a new FTS stability criterion with more accurate synchronized settling time (SST) is studied. Besides, an innovative FTS controller is proposed by the norm normalized (NN) sign function, and the chattering caused by the traditional sign function is weakened. As an application, we study the FTS stabilization of chaotic systems through a new controller. Finally, two numerical examples show the effectiveness and efficiency of the theoretical analysis results.