Finite-Time Convergence and Robustness Analysis of Two Nonlinear Activated ZNN Models for Time-Varying Linear Matrix Equations

Based on zeroing neural network (ZNN), this paper designs two nonlinear activated ZNN (NAZNN) models for time-varying linear matrix equation through taking two new activation functions into consideration. The purpose of constructing the novel models is to solve the problem of time-varying linear matrix equation quickly and precisely. Theoretical analysis proves that two new activation functions can not only accelerate the convergence rate of the prime ZNN models but also come true finite-time convergence. After adding differential error and model-implementation error into the models, the theoretical upper bounds of the steady state residual errors are calculated, which demonstrate the superior robustness of the proposed two NAZNN models. Finally, comparative simulation results show the excellent performance of the proposed two NAZNN models by solving time-varying linear matrix equation.