Continuous and discrete zeroing neural dynamics handling future unknown-transpose matrix inequality as well as scalar inequality of linear class

摘要

In this paper, the future unknown-transpose matrix inequality (FUTMI) as well as scalar inequality is formulated and investigated for the first time. This particular class of inequality may be encountered in scientific researches or engineering fields. In order to solve this intricate and complex problem, the corresponding continuous unknown-transpose matrix inequality (CUTMI) is formulated and discussed. In addition, a method transforming inequality into equality equivalently is introduced. Then, zeroing neural dynamics (ZND) is applied to the CUTMI solving, and a novel ZND model termed continuous-time ZND (CTZND) model is proposed and investigated. Furthermore, by adopting the Euler forward formula to discretize CTZND model, a novel discrete-time ZND (DTZND) model for solving FUTMI is derived and analyzed. Theoretical analysis indicates that the proposed DTZND model is zero-stable, consistent, and convergent. Finally, numerical experiment results further substantiate the good effectiveness and accuracy of the proposed CTZND and DTZND models.