Time-Variant and Time-Invariant Matrix Inequations of Zhang Equivalency Besides Matrix Equations

Via the paper, the ZE (Zhang equivalency) concept is firstly revisited, and then, on the basis of ZE, equation-type ZE and inequation-type ZE are further showed and discussed. By utilizing ZND (i.e., Zhang neural dynamics) method, we present the general expressions of equation-type ZE, and apply them in seven types of time-variant matrix situations. Then, we further discuss the inequation-type ZE and present the order-l (i.e, 01), order-2 (i.e, 02), and order-3 (i.e, 03) general expressions of inequation-type ZE. By utilizing these expressions, we hence propose the 01, 02, and 03 expressions of inequation-type ZE in six types of matrix situations for handling corresponding time-variant matrix inequation problems.