Multiple exponential stability and instability for state-dependent switched neural networks with time-varying delays and piecewise-linear radial basis activation functions

This paper formulates multiple exponential stability and instability for a class of state-dependent switched neural networks (NNs) with time-varying delays in two cases of switching threshold W < q and W >= q. Correspondingly, the index set N = {1, 2, center dot center dot center dot , n} is divided into four categories N-1, N-2, N-3, N-4 for W < q and (N) over tilde (1), (N) over tilde (2), (N) over tilde (3), (N) over tilde (4) for W >= q. According to the invariant interval acquired in these four categories, the state space is partitioned into 5(N2#) (4((N) over tilde2#)) regions, where N-2(#) ((N) over tilde (#)(2)) signifies the number of elements in N-2 ((N) over tilde (2)). Together with reduction to absurdity, function continuity and monotonicity, as well as Lyapunov method, sufficient conditions are developed to guarantee there exists a unique equilibrium point in each region and 3(N2#) (3((N) over tilde2#)) equilibrium points are locally exponentially stable, the others are unstable. Three numerical examples are provided to validate the effectiveness of theoretical results. (c) 2022 Published by Elsevier B.V.