International Journal of Computational
Intelligence Research (IJCIR)
Volume 2, Number 1 (2006)
Delayed standard neural network models for the stability analysis
of recurrent neural networks
College of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
In order to conveniently analyze the stability of recurrent neural networks (RNNs), similar to the nominal model in robust control, the novel neural network model, named delayed standard neural network model (DSNNM) is advanced, which is the interconnection of a linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. By combining a number of different Lyapunov functionals with S-Procedure, some useful criteria of global asymptotic stability and global exponential stability for the continuous-time DSNNMs are derived, whose conditions are formulated as linear matrix inequalities (LMIs). Most delayed (or non-delayed) RNNs can be transformed into the DSNNMs to be stability analyzed in a unified way. Finally, the application example of the DSNNMs to the stability analysis of the continuous-time delayed RNNs shows that the DSNNMs make the stability conditions of the RNNs easily verified.
Delayed standard neural network model (DSNNM), generalized eigenvalue problem (GEVP), linear matrix inequality (LMI), stability, recurrent neural network