Stability of Hopfield Neural Networks
Back propagation (BP) neural network is used to approximate the dynamic character of nonlinear discrete-time
system. Considering the unmodeling dynamics of the system, the weights of neural network are updated by using a deadzone
algorithm and a robust adaptive controller based on the BP neural network is proposed. For the situation that jumping
change parameters exist, multiple neural networks with multiple weights are built to cover the uncertainty of parameters, and
multiple controllers based on these models are set up. At every sample time, a performance index function based on the
identification error will be used to choose the optimal model and the corresponding controller. Different kinds of
combinations of fixed model and adaptive model will be used for robust multiple models adaptive control (MMAC). The
proof of stability and convergence of MMAC are given, and the significant efficacy of the proposed methods is tested by
simulation. This paper deals with the problem of delay-dependent stability criterion of delay-difference system with multiple
delays of Hopfield neural networks. Based on quadratic Lyapunov functional approach and free-weighting matrix approach,
some linear matrix inequality criteria are found to guarantee delay-dependent asymptotical stability of these systems. And
one example illustrates the exactness of the proposed criteria.
Keywords - Hopfield neural networks; Time-varying Delay; Stability; Quadratic Lyapunov functional approach.