Complex Double Integration Enhanced ZNN with Rejection of Linear Noise for Computing Time-Dependent Sylvester Equation

Recurrent neural networks (RNN) are highly effective in solving the inverse problem of time-dependent matrices. However, in real-world engineering applications, noise interference is inevitable. The zeroing neural network (ZNN) is a special class of RNN that exhibit strong noise tolerance in solving the time-dependent Sylvester equation (TDSE). Despite the usefulness of the previously proposed original ZNN (OZNN) model and integral enhanced ZNN (IEZNN) model, they lack the ability to suppress linear and quadratic noise when solving the Sylvester equation. In this paper, a complex double integration enhanced ZNN (CDIEZNN) model is introduced for the first time to address the problem of TDSE. The theoretical basis for the convergence and robustness of the double integral model is described in detail. Two experiments are conducted to verify the convergence and robustness of the CDIEZNN model, and the digital simulation results demonstrate that in solving the TDSE, the residual error of the CDIEZNN model rapidly and stably converges to 3.82 × 10– ⁶ in a linear noise environment, and even in complex quadratic noise environments, the residual error can still converge to 1.99 × 10- ² • In contrast, the OZNN and IEZNN models have weak suppression of linear noise and the residual errors cannot converge in a quadratic noise environment and the results show divergence.