Fixed-Time Stabilization of Delayed Discontinuous Fuzzy Neural Networks via Delayed Stability Conditions of Filippov Systems
Fanchao Kong, Quanxin Zhu, Tingwen Huang · IEEE Transactions on Fuzzy Systems · 2022
This article aims to propose time-delayed and simplified inequality conditions and establish more novel fixed-time (FXT) stability principles of delayed Filippov systems. First, the sign function is used to unify the orders of the Lyapunov–Krasovskii functional, and the time-delayed term is introduced in the inequality conditions, then some new FXT stability theorems are established and new estimations of the settling time involving delayed parameter are given that are absolutely different from the previous ones. The traditional inequality conditions$\dot{V}(z)\leq -aV^\alpha (z)-bV^\beta (z)$is optimized and improved. For the purpose of illustrating the applicability, a class of delayed discontinuous fuzzy Cohen–Grossberg neural networks (DDFCGNNs) is studied. Some new criteria are derived, and the FXT stabilization of the addressed DDFCGNNs is achieved. Finally, a representative example and simulations are provided to examine the correctness.