A New Fixed-Time Stability Criterion and Its Application to Synchronization Control of Memristor-Based Fuzzy Inertial Neural Networks with Proportional Delay

In this paper, a new criterion related to fixed-time stability is derived by strict mathematical techniques such as definite integral and inequality techniques. Compared with the existing theorems, the estimate of upper bound for settling time is smaller, which is not only proved theoretically but also shown by numerical simulations. And the new criterion gets improved after introducing a new lemma. Then on the basis of the new criterion and the improved theorem, the fixed-time synchronization (FTS) of a memristor-based fuzzy inertial neural network (MFINN) with proportional delay is investigated via adopting a delay-dependent feedback controller, and several sufficient conditions are given for the FTS of the MFINN. At last, numerical simulations are raised to substaintiate the correctness of our theoretical results.