Five-Node ZeaD Formula and Zeroing-Dynamics Model Applied to Generalized-Sylvester-Type Future Linear Matrix Inequality
Zhiyuan Qi, Yang Shi, Jian Li, Mingzhi Mao, Yunong Zhang · 2019
In this paper, a new discrete-time zeroing-dynamics (or termed, Zhang-dynamics, ZD) model is proposed, analyzed and investigated for solving generalized-Sylvester-type future linear matrix inequality (GS-type FLMI). First of all, based on ZD design formula, a continuous-time ZD (CTZD) model, i.e., CTZD-I model, is proposed for solving generalized-Sylvester-type continuous-time linear matrix inequality (GS-type CTLMI). Secondly, a five-node Zhang et al discretization formula (ZeaD formula, also termed Zhang et al time-discretization or Zhang time-discretization [ZTD] formula) is presented for the first-order derivative approximation with higher computational precision. Then, by exploiting the presented ZeaD formula, a novel discrete-time ZD (DTZD) model, i.e., ZeaD-type DTZD-I model, is proposed, analyzed and investigated for solving GS-type FLMI. Theoretical analyses on the convergence and precision of the proposed ZeaD-type DTZD-I model are presented. Comparative numerical experimental results further substantiate the efficacy and superiority of proposed ZeaD-type DTZD-I model.