Some New Stability Properties of Dynamic Neural Networks With Different Time-Scales

Abstract

Dynamic neural networks with different time-scales include the aspects of fast and slow phenomenons. Some applications require that the equilibrium points of these networks to be stable. The main contribution of the paper is that Lyapunov function and singularly perturbed technique are combined to access several new stable properties of different time-scales neural networks. Exponential stability and asymptotic stability are obtained by sector and bound conditions. Compared to other papers, these conditions are simpler. Numerical examples are given to demonstrate the effectiveness of the theoretical results.

Identification of singularly perturbed nonlinear system using recurrent high-order neural network

“…System identification via multilayer RNN with two time scales are proposed in [3] later. In [4,5,6], the stability properties of RNN with different time scales are discussed. Robustness stability results for uncertain two-time scale RNN under parameter perturbations are established in [7].…”

“…Robustness stability results for uncertain two-time scale RNN under parameter perturbations are established in [7]. It should be pointed out that most research done before regarding identification of nonlinear system using RNN with different time scales are based on continuous systems [1][2][3][4][5][6][7]. However, the identification and control of discrete time systems using multi-time scale NN are seldom considered in the control community.…”