In practice, Multi Variable Control (MVC) is very close of Process Control, which is a discipline of most interest for Chemical Engineering. Since Chem. Engs are usually not very deeply trained in "Advanced Maths" (at least in my country this is the case...) you often get very readable tutorials/book chapters on some Control areas focused on Chem. Engs. This happens for instance with Nonlinear Control and MPC (Model Predictive Ctrl.).
IDK what is your reading text, so here go some suggestions.
So, my first suggestion is to find a Process Control book and read the couple of chapters on MVC. As today, you can find online the 2nd edition of "Process Dynamics & Control" from Seborg et. al. and the 18th chapter has a good introduction. This is a widely used book in Chem. Eng. courses. IMHO this will be a good introduction.
For a more deep reading, you have online (legally, AFAIK) the 2nd edition of "Process Control, Designing Processes and Control Systems for Dynamic Performance" from Marlin in http://pc-textbook.mcmaster.ca/ where Part V (~150 pages) is devoted to MPC. This is a solid read, and is also a widely used book in Chem. Eng. courses.
The reference text on MVC today is IMHO ( https://www.amazon.com/Multivariable-Feedback-Control-Analysis-Design/dp/0470011688/ ) I have the 1st edition, and is quite good, 500 pages or so of MVC. You can also find it online. It is a book where theory is solidly explained.
Besides this there are many other texts on MVC; for instance, Springer has published quite a bunch of them (search online book sellers to find them). For instance, you can find "MVC: an engr. approach" from Albertos & Sala ( https://www.amazon.com/Multivariable-Control-Systems-Engineering-Processing/dp/1852337389/ ) online. Ihave this book and is quite good.
There are also some introduction/tutorial papers, such as:
https://authors.library.caltech.edu/93676/1/01102555.pdf
Good luck...
I like Skogestad for the basics Multivariable Feedback Control And Khalil for the more advanced Nonlinear Systems