Finite-time Convergent Complex-Valued Neural Networks for the Time-varying Complex Linear Matrix Equations

摘要

In this paper, we propose two complex-valuedneural networks for solving a time-varying complex linearmatrix equation by constructing two new types of nonlinearactivation functions. Theoretically, we prove that the complexvalued neural networks are globally stable in the sense ofLyapunov stability theory. The solution of the complex-valuedneural networks converges to the theoretical solution of thetime-varying complex linear matrix equation in finite time.Compared with existing real-valued neural networks for solvingtime-varying complex linear matrix equations, the complexvalued neural nerworks can avoid redundant computation in adouble real-valued space and thus has a low model complexityand storage capacity. Numerical simulations are presented toshow the effectiveness of the complex-valued neural networks.