Finite-time stabilization control of memristor-based neural networks

This paper investigates the finite-time stabilization problem for a general class of memristor-based neural networks (MNNs). Firstly, based on set-valued analysis and Kakutani's fixed point theorem of set-valued maps, the existence of equilibrium point can be guaranteed for MNNs. Then, by designing novel discontinuous controller, some sufficient conditions are proposed to stabilize the states of such MNNs in finite time. Moreover, we give the upper bound of the settling time for stabilization which depends on the system parameters and control gains. The main tools to be used involve the framework of Filippov differential inclusions, non-smooth analysis, matrix theory and the famous finite-time stability theorem of nonlinear system. Finally, the theoretical results are verified by concrete examples with computer simulations.