Finite-time robust synchronization for discontinuous neural networks with mixed-delays and uncertain external perturbations

Abstract

Abstract This paper investigates the finite-time robust synchronization problem of mixed time-delayed neural networks (DNNs) with discontinuous activations and uncertain external perturbations. Two classes of simple discontinuous controllers (i.e., switching state-feedback controller and switching adaptive controller) are designed such that the response system can be finite-time robustly synchronized with a drive system. Without using the well-known finite-time stability theorem given by Forti in 2006, the finite-time robust synchronization control of discontinuous DNNs can be realized via generalized Lyapunov–Krasovskii functionals approach and novel analysis techniques. Moreover, the upper bounds of the settling time for synchronization are estimated. The main tools of this paper involve functional differential inclusion theory in the sense of Filippov solutions and non-smooth analysis. Finally, two numerical examples are provided to illustrate the effectiveness of the designed control method and the theoretical results.