Future Linear Matrix Equation of Generalized Sylvester Type Solved by Zeroing Neural Dynamics and 5-Instant ZeaD Formula

In this paper, a new discrete-time zeroing dynamics (or say, Zhang dynamics, ZD) model is proposed, analyzed and investigated for solving generalized-Sylvester-type future linear matrix equation (GS-type FLME). First of all, based on ZD design formula, a continuous-time ZD (CTZD) model is proposed for solving generalized-Sylvester-type continuous-time linear matrix equation (i.e., GS-type CTLME). Secondly, a novel one-step-ahead discretization formula (termed Zhang et al. discretization formula, ZeaD formula) is presented for the first-order derivative approximation with higher computational precision. Then, by exploiting the presented ZeaD formula to discretize the CTZD model, a novel discrete-time ZD (DTZD) model, i.e., ZeaD-type DTZD-E model, is proposed, analyzed and investigated for solving GS-type FLME. Theoretical analyses on the convergence and precision of the proposed DTZD models are presented. Comparative numerical experimental results further substantiate the efficacy and superiority of proposed ZeaD-type DTZD model for solving the GS-type FLME.