Robust stabilising controller synthesis for discrete-time recurrent neural networks via state feedback

This paper addresses the stabilisation problem of discrete-time recurrent neural networks (RNNs) containing norm-bounded uncertainties. A novel neural network model, named standard neural network model (SNNM), is used to provide a general framework for robust stabilising controller synthesis of RNNs. Most of the existing RNNs can be transformed into SNNM to be synthesised in a unified way. Applying the Lyapunov stability theory and the S-procedure technique, state feedback controllers are designed to guarantee the global asymptotical stability of closed-loop dynamic discrete-time systems. The controller gains are obtained by solving a set of linear matrix inequalities. Examples are given to illustrate the transformation procedure and the effectiveness of the proposed design technique.