A novel fixed-time stability lemma and its application in the stability analysis of BAM neural networks

In this paper, we put forward an interesting fixed-time (FXT) stability lemma, which is based on a whole new judging condition, and the minimum upper bound for the stability start time is obtained. In the new FXT stability lemma, the mathematical relation between the upper bound of the stability start time and the system parameters is very simple, and the judgment condition only involves two system parameters. To indicate the usability of the new FXT stability lemma, we utilize it to study the FXT stability of a bidirectional associative memory neural network (BAMNN) with bounded perturbations via sliding mode control. To match the developed FXT stability lemma, novel sliding mode state variables and a two-layer sliding mode controller are designed. According to the developed FXT stability lemma, the perturbed BAMNN can achieve FXT stability under the devised sliding mode controller. The upper bound of the stability start time can be calculated easily by virtue of the control parameters, and the sufficient conditions guaranteeing that the perturbed BAMNN can achieve FXT stability have also been derived. Last, we provide some confirmatory simulations.