Multiple O(t-α) stability for fractional-order neural networks with time-varying delays

In this paper, the multiple O(t(-alpha)) stability for fractional-order neural networks (FoNNs) with time-varying delays is formulated and explored. According to n pairs of bounded functions, which are obtained from FoNNs model as well as the maximum and minimum values of the activation functions, state space is partitioned into Pi(n)(i=1)(2M(i) + 1) parts, where M-i >= 0 is a nonnegative integer and is determined by bounded functions. Sufficient conditions are acquired to guarantee the existence of Pi(n)(i=1)(M-i + 1) O(t(-alpha)) stable equilibrium points. The obtained criteria generalize and extend the existing results. Several illustrative examples are raised to confirm the effectiveness of the theoretical results. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.