Fixed-/preassigned-time synchronization control of discontinuous inertial fuzzy neural networks with time delays

This paper aims to explores the fixed-/preassigned-time synchronization for delayed inertial fuzzy Hopfield neural networks with discontinuous activations. First, in light of a new variable substitution, the original second-order system is transformed into the first-order differential equation. Next, by designing a novel negative-feedback controllers and constructing a general Lyapunov function, with the help of the Filipov discontinuity theory, a number of novel and flexible fixed-time synchronization criteria are obtained for the established system and the upper-bound of the setting time is more explicitly estimated as well. Moreover, the preassigned-time synchronization of considered system is further investigated, in which the settling time can be prespecified and independent of the initial value and parameters. The obtained theoretical results extend and improve some existing outcomes. Eventually, numerical simulations are conducted to verify the correctness of the obtained results.