Two finite-time convergent Zhang neural network models for time-varying complex matrix Drazin inverse

Abstract

This paper concerns the computation of the Drazin inverse of a complex time-varying matrix. Based on two Zhang functions constructed from two limit representations of the Drazin inverse, we present two complex Zhang neural network (ZNN) models with the Li activation function for computing the Drazin inverse of a complex time-varying square matrix. We prove that our ZNN models globally converge in finite time. In addition, upper bounds of the convergence time are derived analytically via the Lyapunov theory. Our simulation results verify the theoretical analysis and demonstrate the superiority of our ZNN models over the gradient-based GNN models.