Delay‐Range‐Dependent Global Robust Passivity Analysis of Discrete‐Time Uncertain Recurrent Neural Networks with Interval Time‐Varying Delay

Abstract

This paper examines a passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. Based on an appropriate type of Lyapunov functional, sufficient passivity conditions for the DRNNs are derived in terms of a family of linear matrix inequalities (LMIs). Two numerical examples are given to illustrate the effectiveness and applicability.

Passivity analysis for discrete-time switched neural networks with various activation functions and mixed time delays

“…Remark 2 All the passivity conditions for the delayed neural networks in [19][20][21][22][23] assume the same activation function. To facilitate the design of neural networks, it is important to consider the neural networks with various activation functions.…”

“…Due to its theoretical importance, the passivity problem for neural networks with time delays has attracted increasing attention. See, for example, [19][20][21][22][23]. In [21], the delay-dependent passivity conditions were proposed for the uncertain neural networks with time-varying discrete delay.…”

“…See, for example, [19][20][21][22][23]. In [21], the delay-dependent passivity conditions were proposed for the uncertain neural networks with time-varying discrete delay. In [23], the authors provided some delay-dependent passivity conditions for the uncertain discrete-time neural networks with mixed time delays.…”

Robust Stochastic Stabilization and H ∞ Control for Neutral Stochastic Systems with Distributed Delays

“…In [13], the problem of H ∞ output feedback control for uncertain stochastic systems with time-varying delays was studied. In [6], H ∞ control for discrete-time uncertain recurrent neural networks with interval time-varying delay is studied. In [2], robust H ∞ filter design for neutral stochastic uncertain system was proposed, but its result is delay-independent.…”

Improved robust stability criteria for neural networks with fast time-varying delays

“…Among the several methods used to analyse the stability of delay-dependent systems, the free-weighting matrix approach has been shown to be very effective and it provides a less conservative stability result. Some recent results are reported in [17][18][19] and [41,42] on classes of stochastic NNs. This paper considers the problem of robust global stability criteria for uncertain neural networks (UNNs) with time-varying delays.…”