Infinitely many Zhang functions resulting in various ZNN models for time-varying matrix inversion with link to Drazin inverse

• The notion of infinitely many ZFs is proposed for the first time.
• The novel general-form ZNN (NGFZNN) is developed for solving the ZMI problem.
• A link between the ZMI and the Drazin inverse is discovered and presented.
• The NGFZNN model is generalized to solve for the time-varying Drazin inverse (TVDI).

In this Letter, by generalizing the notion of Zhang functions (ZFs) from previous work, a novel general-form Zhang function (NGFZF) is proposed, developed and investigated. Specifically, based on the NGFZF, infinitely many ZFs (as error functions) can be readily generated by successively selecting the different values of its parameters. Besides, by employing the NGFZF, a novel general-form Zhang neural net (NGFZNN) is proposed and studied for real-time solution of a time-varying matrix inverse (also termed, Zhang matrix inverse, ZMI). Moreover, a link between ZMI and Drazin inverse is discovered and further generalized to solve for the time-varying Drazin inverse (TVDI).