On stability of nonlinear continuous-time neural networks with delays

Abstract

We utilize the Lyapunov function method to analyze stability of continuous nonlinear neural networks with delays and obtain some new sufficient conditions ensuring the globally asymptotic stability independent of delays. Three main conditions imposed on the weighting matrices are established. (i). The spectral radius ρ( M −1(| W 0|+| W τ |) K)<1. (ii). The row norm ‖ M −1(| W 0|+| W τ |) K+ P −1((| W 0|+| W τ |) KM −1) T P‖ ∞<2. (iii). μ 2( W 0)+‖ W τ ‖ 2, F <( m/ k). These three conditions are independent to each other. The delayed Hopfield network, Bidirectional associative memory network and cellular neural network are special cases of the network model considered in this paper. So we improve some previous works of other researchers.