Generalized Finite-Time Stability and Stabilization for Fractional-Order Memristive Neural Networks

This paper is concerned with the generalized finite-time stability, boundedness and stabilization for fractional-order memristive neural networks (FMNNs) with the fractional-order 0 < α < 1. Under the fractional-order Filippov differential inclusion frame, FMNNs are modelled as a fractional-order differential equation with discontinuous right-hand. Based on the topological degree property, the existence of equilibrium point of FMNNs is proved. By means of the generalized Gronwall inequality, the Laplace transform and the Lyapunov functional candidate, some conditions to guarantee the generalized finite-time stability and boundedness for FMNNs are derived in terms of linear matrix inequalities (LMIs). In addition, by using appropriate feedback controller, the generalized finite-time stabilization condition is also addressed in forms of LMIs. Finally, two examples are given to demonstrate the validity of the theoretical results.