\mathscrL₂–\mathscrL_\infty learning of dynamic neural networks

This paper proposes an \mathscrL₂–\mathscrL_\infty learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the \mathscrL₂–\mathscrL_\infty learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an \mathscrL₂–\mathscrL_\infty induced norm constraint. It is shown that the design of the \mathscrL₂–\mathscrL_\infty learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.