Global exponential stability and global convergence in finite time of delayed neural networks with infinite gain

By Mauro Forti, Paolo Nistri, Duccio Papini. IEEE Transactions on Neural Networks, 2005

332 citations recorded by the source corpus.

This paper introduces a general class of neural networks with arbitrary constant delays in the neuron interconnections, and neuron activations belonging to the set of discontinuous monotone increasing and (possibly) unbounded functions. The discontinuities in the activations are an ideal model of the situation where the gain of the neuron amplifiers is very high and tends to infinity, while the delay accounts for the finite switching speed of the neuron amplifiers, or the finite signal propagation speed. It is known that the delay in combination with high-gain nonlinearities is a particularly harmful source of potential instability. The goal of this paper is to single out a subclass of the considered discontinuous neural networks for which stability is instead insensitive to the presence of a delay. More precisely, conditions are given under which there is a unique equilibrium point of the neural network, which is globally exponentially stable for the states, with a known convergence rate. The conditions are easily testable and independent of the delay. Moreover, global convergence in finite time of the state and output is investigated. In doing so, new interesting dynamical phenomena are highlighted with respect to the case without delay, which make the study of convergence in finite time significantly more difficult. The obtained results extend previous work on global stability of delayed neural networks with Lipschitz continuous neuron activations, and neural networks with discontinuous neuron activations but without delays.

Subfields: Computer Networks and Communications, Electrical and Electronic Engineering, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e7007a973684e3fa91bab2a0d7a321a0e22e8c99

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

1. Xinsong Yang
2. Huaguang Zhang
3. Zhanshan Wang
4. Derong Liu
5. Jinde Cao
6. Zhiyou Wu
7. Wenwu Yu
8. Guanrong Chen

In Electrical and Electronic Engineering

1. Derong Liu
2. Huaguang Zhang
3. Zhanshan Wang
4. Xinsong Yang
5. Jinde Cao
6. Qinglai Wei
7. Frank L. Lewis
8. Hamidreza Modares

In Statistical and Nonlinear Physics

1. Xinsong Yang
2. Huaguang Zhang
3. Zhanshan Wang
4. Derong Liu
5. Jinde Cao
6. Zhiyou Wu
7. Jun Wang
8. Wenwu Yu

Citations in the corpus

• Finite-time synchronization of complex networks with nonidentical discontinuous nodes (2013, background): “Compared with infinite-time convergence for smooth dynamical systems, finite-time convergence is especially desirable in global optimization [9, 11].”
• Global Asymptotical Stability of Recurrent Neural Networks With Multiple Discrete Delays and Distributed Delays (2006, background): “881488 of neural network models with discrete time-delays can be found in [3]–[15] and some references cited therein.”
• A Comprehensive Review of Stability Analysis of Continuous-Time Recurrent Neural Networks (2014, background): “6) Discontinuous activation functions [68], [71], [72], [116], [173], [175], [183], [184], [216], [263]: Let g i (·) be a continuous nondecreasing function, and in every compact set of real space R, each g i (·) has only finite discontinuity points.”