Complex-valued Zhang neural network for online complex-valued time-varying matrix inversion

In this paper, a new complex-valued recurrent neural network (CVRNN) called complexvalued Zhang neural network (CVZNN) is proposed and simulated to solve the complexvalued time-varying matrix-inversion problems. Such a CVZNN model is designed based on a matrix-valued error function in the complex domain, and utilizes the complex-valued first-order time-derivative information of the complex-valued time-varying matrix for online inversion. Superior to the conventional complex-valued gradient-based neural network (CVGNN) and its related methods, the state matrix of the resultant CVZNN model can globally exponentially converge to the theoretical inverse of the complex-valued timevarying matrix in an error-free manner. Moreover, by exploiting the design parameter c > 1, superior convergence can be achieved for the CVZNN model to solve such complex-valued time-varying matrix inversion problems, as compared with the situation without design parameter c involved (i.e., the situation with c 1⁄4 1). Computer-simulation results substantiate the theoretical analysis and further demonstrate the efficacy of such a CVZNN model for online complex-valued time-varying matrix inversion. 2011 Elsevier Inc. All rights reserved.