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

Authors: Jianhai Zhang, Huaixiang Zhang, Guojun Dai, Senlin Zhang, Meiqin Liu

Addresses: College of Computer, Hangzhou Dianzi University, Hangzhou, 310018, China. ' College of Computer, Hangzhou Dianzi University, Hangzhou, 310018, China. ' College of Computer, Hangzhou Dianzi University, Hangzhou, 310018, China. ' College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China. ' College of Electrical Engineering, Zhejiang University, Hangzhou, 310027, China

Abstract: 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.

Keywords: standard neural network model; SNNM; robust stabilisation; state feedback; recurrent neural networks; RNN; discrete time systems; linear matrix inequality; LMI; robust control.

DOI: 10.1504/IJMIC.2010.035277

International Journal of Modelling, Identification and Control, 2010 Vol.11 No.1/2, pp.35 - 43

Published online: 20 Sep 2010 *

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