Study On Stability Of Recurrent Neural Networks With Perturbation

Recently, the stability theory of recurrent neural networks is one of the hot topics in the field of neural networks. In the implement of neural networks, perturbation can not be avoided. When perturbation is imported, recurrent neural networks may have more complicated dynamic characteristic. In the mean while, perturbation will affect the application of recurrent neural networks. Recurrent neural networks may not be stable under perturbation so that they will not statisfy the need of application. Thus the study of stability of recurrent neural networks with perturbation has important meaning in theory and practice. The stability of recurrent neural networks with parameter perturbation and time delay will be studied in this dissertation in order to obtain effective stability criteria. This dissertation will provide a theoretical basis for the application of recurrent neural networks and promote the development of the stability theory of recurrent neural networks.First, the Lyapunov functional and variation of constants method are adopted to study the effect that Sigmoid function and the relation of resistance, capacitance and current in Hopfield neural networks have on the stability of networks. The stability criterion constructed by physics parameters is obtained. Thus how the constrained relation of physics parameters affects the stability of Hopfielf neural networks is clear. Based on the study above, the perturbation model of recurrent neural networks is constructed. And the theorems of the existence of solution of perturbation model are presented.Furthermore, time delay can be seen as a perturbation. The effect that time delay has on the stability of recurrent neural networks is considered. Using LaSalle invariance principle and Lyapunov functional, the stability of delayed recurrent neural networks is studed. And the delay-independent stability criterion and delay-dependent stability criterion are obtained respectively. These criteria have muti-parameters which can be adjusted. Thus these criteria are easy to be used for the implement of recurrent neural networks. Considering the effect that parameter perturbation has on the stability of recurrent neural networks, the robust stability of recurrent neural networks with parameter perturbation is studied. Lyapunov functional are used to obtain the robuststability condition of recurrent neural networks with immovable equilibrium point. Using matrix measure, the robust stability of recurrent neural networks with movable equilibrium point is studied. Corresponding robust stability criteria are obtained without the use of Lyapunov functional. Thus a new approach is provided for the robust stability study of recurrent neural networks.Finally, considering the existence of both parameter perturbation and time varying delay in the implement of recurrent neural networks, the globally robust stability of recurrent neural networks with time varying delay and parameter perturbation is studied, using Lyapunov functional and linear matrix inequality. A series of robust stability criteria are obtained. These criteria are in form of linear matrix inequality. Thus it is convenient to validate the robust stability of recurrent neural networks using these criteria. In addition, considering the move of equilibrium point caused by parameter perturbation and time delay, the offset of equilibrium point is estimated in order to guarantee that the equilibrium point satisfies the need of design.