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

Abstract

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,⋯,n} is divided into four categories N1,N2,N3,N4 for W<q and Ñ1,Ñ2,Ñ3,Ñ4 for W⩾q. According to the invariant interval acquired in these four categories, the state space is partitioned into 5N2♯ (4N2̃♯) regions, where N2♯ (N2̃♯) signifies the number of elements in N2 (N2̃). 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 3N2♯(3Ñ2♯) equilibrium points are locally exponentially stable, the others are unstable. Three numerical examples are provided to validate the effectiveness of theoretical results.