Taylor-Type Direct-Discrete-Time Integral Recurrent Neural Network with Noise Tolerance for Discrete-Time-Varying Linear Matrix Problems with Symmetric Boundary Constraints

Various types of noise interference often challenge the solution of discrete time-varying linear matrix problems with boundary constraints in practical engineering applications. To address this issue, this paper proposes a Taylor-type direct-discrete-time integral noise-immune recurrent neural network (TD-IRNN) model. Specifically, the model is constructed by transforming the bounded discrete linear matrix problem into a unified discrete matrix formulation and incorporating an error accumulation term during the design process. The proposed TD-IRNN model not only eliminates the need for continuous-environment conversion but also significantly enhances its noise immunity. Theoretical analysis demonstrates that the model exhibits excellent convergence and stability under different noise conditions. Numerical experiments and a robotic manipulator trajectory tracking experiment further validate the effectiveness and practical applicability of the TD-IRNN model in complex environments.