Novel switching design for finite-time stabilization: Applications to memristor-based neural networks with time-varying delay.

The aim of this paper is to provide a novel switching control design to solve finite-time stabilization issues of a discontinuous or switching dynamical system. In order to proceed with our analysis, we first design two kinds of switching controllers: switching adaptive controller and switching state-feedback controller. Then, we apply the proposed switching control technique to stabilize the states of delayed memristor-based neural networks (DMNNs) in finite time. Based on a famous finite-time stability theorem, the theory of differential inclusion and the generalized Lyapunov functional method, some sufficient conditions are obtained to guarantee the finite-time stabilization control of DMNNs. The feedback functions of our model are allowed to be unbounded, and the upper bounds of the settling time for stabilization are also given. Finally, the validity of designed method and the theoretical results are illustrated by numerical examples.