Robust exponential stability for interval neural networks with delays and non-Lipschitz activation functions

Abstract

In this paper, the global robust exponential stability of interval neural networks with delays and inverse Hölder neuron activation functions is considered. By using linear matrix inequality (LMI) techniques and Brouwer degree properties, the existence and uniqueness of the equilibrium point are proved. By applying Lyapunov functional approach, a sufficient condition which ensures that the network is globally robustly exponentially stable is established. A numerical example is provided to demonstrate the validity of the theoretical results.

Neural networks with distributed delays and Hölder continuous activation functions

“…Non-Lipschitz continuous activation functions arise in many fields [10], see also [6] for an application involving Hölder continuous functions. For a slightly weaker condition or partial Lipschitz condition we refer the reader to [3,4,23,25].…”

p-th moment exponential convergence analysis for stochastic networked systems driven by fractional Brownian motion

“…When applying NNs to solve many practical problems in optimization, NNs are usually designed to be globally asymptotically or exponentially stable to avoid spurious responses or the problem of local minima. Hence, exploring the convergence of NNs is of primary importance; see [6][7][8][9][10][11], and references therein.…”

Stability analysis of neutral type neural networks with mixed time-varying delays using triple-integral and delay-partitioning methods

“…However, time delays as a source of instability and poor performance often appear in many neural networks such as Hopfield neural networks, cellular neural networks, Cohen-Grossberg neural networks and bidirectional associative memory neural networks. Therefore, the stability analysis for delayed neural networks has received substantial attention in recent years (see [15][16][17][18][19][20][21] and the references therein). In general, studying the dynamical behavior of delayed neural networks can be classified into two types: delay-independent stability and delay-dependent stability.…”