Global exponential stability in Lagrange sense for periodic neural networks with various activation functions and time-varying delays

Swati Tyagi ¹   ; Syed Abbas ²   ; Manuel Pinto ³

¹ Indian Institute of Technology Ropar Rupnagar 140001, India
² Indian Institute of Technology Mandi Mandi 175005, India
³ Departamento de Matemáticas Facultad de Ciencias Universidad de Chile Santiago, Chile

Applicationes Mathematicae, Tome 46 (2019) no. 2, pp. 229-252

Résumé

In recent years, the concept of Lyapunov stability has received a remarkable attention in the field of neural networks. However the stability in Lagrange sense for neural networks has not been studied much. It is to be noticed that while Lyapunov stability refers to stability of the equilibrium point, Lagrange stability refers to the stability of the total system. In this paper, we study the global exponential stability in Lagrange sense for periodic neural networks with multiple time delays and more general activation functions including general bounded and sigmoidal type activation functions. By constructing suitable Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. We present a detailed estimation of global exponential attractive sets from the system parameters without any supposition on existence. We investigate whether the equilibrium point of the network system is globally exponentially stable by means of globally exponentially attractive sets. At the end, we give some numerical examples to validate our analytical findings. The results obtained are helpful in designing globally asymptotically stable cellular neural networks and reduce the search domain of optimization.

Détail

DOI : 10.4064/am2320-10-2017

Keywords: recent years concept lyapunov stability has received remarkable attention field neural networks however stability lagrange sense neural networks has studied much be noticed while lyapunov stability refers stability equilibrium point lagrange stability refers stability total system paper study global exponential stability lagrange sense periodic neural networks multiple time delays general activation functions including general bounded sigmoidal type activation functions constructing suitable lyapunov like functions provide easily verifiable criteria boundedness global exponential attractivity periodic neural networks present detailed estimation global exponential attractive sets system parameters without supposition existence investigate whether equilibrium point network system globally exponentially stable means globally exponentially attractive sets end numerical examples validate analytical findings results obtained helpful designing globally asymptotically stable cellular neural networks reduce search domain optimization