Complex Neural Network Models for Time-Varying Drazin Inverse

What is it about?

Two complex Zhang neural network (ZNN) models for computing the Drazin inverse of arbitrary time-varying complex square matrix are presented. The design of these neural networks is based on corresponding matrix-valued error functions arising from the limit representations of the Drazin inverse. Two types of activation functions, appropriate for handling complex matrices, are exploited to develop each of these networks. Theoretical results of convergence analysis are presented to show the desirable properties of the proposed complex-valued ZNN models. Numerical results further demonstrate the effectiveness of the proposed models.

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Why is it important?

Our tendency in this letter is twofold. First, our aim is to define an appropriate ZNN-type model for computing the time-varying Drazin inverse. For this purpose, we define proper Zhang functions and develop initiated ZNN models starting from the limiting representations of the Drazin inverse. Second, our intention is to define a suitable option to avoid constraint imposed on the eigenvalues. Evidently the limit representation provides the best solution.