Fixed-time synchronization of delayed impulsive inertial neural networks with discontinuous activation functions via indefinite LKF method. Issue 2 (January 2022) - Udhayakumar, K.; Shanmugasundaram, S.; Janani, K.; Kathiresan, S.; Rakkiyappan, R.
Abstract: This article investigates the fixed time synchronization (FXTSY) problem of time-varying delayed impulsive inertial neural networks (INNs) with discontinuous activation functions. First, the addressed delayed discontinuous INNs are converted into a first-order differential equation using a generalized variable transformation with suitable tunable variables. Due to the existence of the discontinuities, the delayed discontinuous differential equations are transformed into the differential inclusions by using the differential inclusion theory and set-valued map concepts. Furthermore, by designing the suitable centralized impulsive control and discontinuous control, constructing the novel indefinite type Lyapunov functionals, new algebraic conditions are derived to realize the FXTSY for the leader-following impulsive INNs. Moreover, the settling time is explicitly calculated. Finally, the developed theoretical results are verified by two numerical simulation results.