New Recurrent Neural Network for Different-Level Sylvester Matrix Equation System: A Direct Discrete Architecture Perspective

Discrete time-varying problems are pervasive in the fields of engineering and science. Traditional handling schemes to discrete problem often involve the intervention of continuous-time frameworks, and, to some extent, there is a lack of independent handling scheme in the discrete-time frameworks. Evidently, the theoretical limitation of existing handling schemes significantly restricts the theoretical exploration and practical application of discrete time-varying problem. In this paper, a new direct-discrete-architecture recurrent neural network model is proposed, analyzed, and investigated for solving discrete time-varying different-level Sylvester matrix equation system, which is the deeper manifestation of a fundamental problem in the mathematical and engineering field. Note that the proposed direct-discrete-architecture recurrent neural network model relies on direct discrete architecture perspective, which is a derivation method of recurrent neural network that is independent of continuous-time frame. Theoretical analysis is conducted to demonstrate the convergence and accuracy of the proposed direct-discrete-architecture recurrent neural network model. Moreover, two numerical experiments targeting different problems validate the excellent performance of the proposed direct-discrete-architecture recurrent neural network model.