Double integral‐enhanced Zeroing neural network with linear noise rejection for time‐varying matrix inverse

Abstract In engineering fields, time‐varying matrix inversion (TVMI) issue is often encountered. Zeroing neural network (ZNN) has been extensively employed to resolve the TVMI problem. Nevertheless, the original ZNN (OZNN) and the integral‐enhanced ZNN (IEZNN) usually fail to deal with the TVMI problem under unbounded noises, such as linear noises. Therefore, a neural network model that can handle the TVMI under linear noise interference is urgently needed. This paper develops a double integral‐enhanced ZNN (DIEZNN) model based on a novel integral‐type design formula with inherent linear‐noise tolerance. Moreover, its convergence and robustness are verified by derivation strictly. For comparison and verification, the OZNN and the IEZNN models are adopted to resolve the TVMI under multiple identical noise environments. The experiments proved that the DIEZNN model has excellent advantages in solving TVMI problems under linear noises. In general, the DIEZNN model is an innovative work and is proposed for the first time. Satisfyingly, the errors of DIEZNN are always less than 1 × 10−3 under linear noises, whereas the error norms of OZNN and IEZNN models are not convergent to zero. In addition, these models are applied to the control of the controllable permanent magnet synchronous motor chaotic system to indicate the superiority of the DIEZNN.