Stability Analysis of Neutral-Type Cohen-Grossberg Neural Networks With Multiple Time-Varying Delays

Abstract

This paper deals with the problem for stability of neutral-type Cohen-Grossberg neural networks involving delay parameters. In the neutral-type neural networks, the states of the neurons involve multiple time-varying delays and time derivative of states of neurons include discrete time delays. We note that the neutral-type neural network cannot be expressed in the vector-matrix form due to multiple time-varying delays and discrete neutral delays, which leads to linear matrix inequality approach can not be employed to obtain stability conditions of this type of Cohen-Grossberg neural networks. Therefore, it is difficult for stability analysis of this type of Cohen-Grossberg neural networks to find suitable Lyapunov-Krasovskii functional and effective method. This paper constructs an appropriate Lyapunov-Krasovskii functional and employs M-matrix property to derive new sufficient conditions ensuring the global asymptotic stability of the equilibrium point of the neutral-type Cohen-Grossberg neural networks with multiple time-varying delays in the states and discrete delays in the time derivative of the states. The obtained stability conditions are easy to validate by testing basic matrix property. A constructive example is presented to indicate applicability of the obtained stability criteria. Compared with the existed references, the networks we studied are more general and the derived results develop and generalize the known results.