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.

Automated summary

This paper formulates multiple exponential stability and instability for a class of state-dependent switched neural networks with time-varying delays. It divides the index set into different categories based on the switching threshold. By obtaining the invariant intervals in these categories, the state space is partitioned into multiple regions. By applying reduction to absurdity, function continuity and monotonicity, as well as Lyapunov method, the paper establishes sufficient conditions for the existence of unique equilibrium points in each region and their stability properties.