Two Discrete ZNN Models for Solving Time-Varying Augmented Complex Sylvester Equation

Abstract Based on practical applications of the complex-valued Sylvester equation and the effectiveness of zeroing neural network (ZNN) in solving time-varying problems, two discrete nonlinear and noise-tolerant ZNN (DNN-TZNN) models are proposed to solve the time-varying augmented complex Sylvester (TACS) equation by using the Adams-Bashforth formula to discretize the continuous nonlinear and noise-tolerant ZNN (CNN-TZNN) model. The presented DNN-TZNN models are divided into two types: DNN-TZNK and DNN-TZNU models, according to whether the derivative information is known or not in the CNN-TZNN design formula. Compared with the continuous ZNN methods, the proposed DNN-TZNN models are more innovative, and compared with other discrete ZNN methods, the convergence speed of the DNN-TZNN models is much faster and more accurate. Through the theoretical analysis, the superior convergence and strong robustness of the DNN-TZNN models are guaranteed. At last, the simulative experiments not only verify the correctness of the theoretical analysis but also demonstrate the availability of the DNN-TZNN models in solving the TACS problem.