Convergence of diagonal recurrent neural networks' learning

Due to disagreement with the proof of convergence theorems of diagonal recurrent neural networks (DRNN) for MISO systems given by Ku and Lee (1995), modified proofs are presented in this paper. Meanwhile, since the output error(s) are the function(s) of all the weights in DRNNs, it is irrational to update part of the weights while the others are kept invariable. Therefore convergence theorems for MISO systems should be modified in the way of putting all the weights into one variable vector. In addition, a convergence theorem of DRNNs for MIMO systems is developed.