The Gaussian error function for a new theorem on fixed-time stability with applications in synchronization of chaotic Lorenz systems

This paper introduces a new fixed-time stability theorem using the Gauss error function and some inequality techniques. Unlike the existing fixed-time stability theorems, the proposed criterion and the formula for estimating the upper bound for the settling time are different. The developed fixed-time stability criteria are then applied to achieve the fixed-time synchronization of chaotic Lorenz systems by designing a feedback controller. Finally, some examples are given to demonstrate the effectiveness of the obtained results.