For automotive applications, a good reference is Del Re L, Allgöwer F, Glielmo L, et al. Automotive model predictive control[J]. LNCIS, 2010, 402: 1-22.
For the basic theorem, a good reference is Wang L. Model predictive control system design and implementation using MATLAB®[M]. Springer Science & Business Media, 2009.
I completely agree with Sylvain Bertrand. The book of Prof. Rawlings and Prof. Mayne is an excellent and relatively updated book for MPC researchers and practitioners. Nevertheless, I would rather pick a different book to start since this book could be tough at the beginning. In this sense you could use the book of Rossiter or the book of Camacho.
(1) Usually the lecture notes can help us understand the basic concepts of new theory more quickly.
[Gawthrop08] Peter Gawthrop, "From Smith's predictor to model-based predictive control," Lecture Notes, University of Glasgow, 2008. Available from the following link.
Only Smith Predictor and PID Control were listed in the “Leaders of the Pack” InTech’s 50 most influential industry innovators since 1774. Available from the following link.
http://archive.today/2RoSK
Otto J.M. Smith and Smith Predictor
PID Control was listed twice (the dominant control method in the industrial applications) -- (1) John G. Ziegler and Nathaniel B. Nichols and classical PID Control; (2) Karl Johan Astrom and modern PID Control (IEEE Medal of Honor, 1993).
[Bemporad09] A. Bemporad, "Model Predictive Control: Basic Concepts," Lecture Notes, Controllo di Processo e dei Sistemi di Produzione, 2009. Available from the following link.
Bemporad states that "Unconstrained linear MPC is nothing else than a standard linear state-feedback law!"
The paper [HY07] applies a standard linear state-feedback law for Internet congestion control.
[HY07] Y. Hong and O.W.W. Yang, "Self-Tuning Optimal PI Rate Controller for End-to-End Congestion With LQR Approach," Proceedings of 20th International Teletraffic Congress (ITC-20), Ottawa, Canada, June 2007, pp.829-840. Available from the following RG Link.
The technical report [Hong99] presents a general control system design based on the standard linear state-feedback law.
[Hong99] Y. Hong, “The Controller Design For Linear System: A State Space Approach,” Technical Report, National University of Singapore, November 1999. DOI: 10.13140/RG.2.2.21548.21120/1 Available from the following RG link.
Preprint The Controller Design For Linear System: A State Space Approach
(2) The textbook [RM15] suggested by Sylvain Bertrand, Ahmed Chemori and Martin Gulan can be downloaded from the following link.
http://jbrwww.che.wisc.edu/home/jbraw/mpc/
[RM15] J.B. Rawlings and D.Q. Mayne, "Model predictive Control: Theory and Design", 5th Edition, Nob Hill Publishing, LLC, 2015.
To celebrate the golden anniversary, The International Federation of Automatic Control (IFAC) Automatica has published in the 50th volume throughout the year 2014, special survey/overview papers, on selected topics, some tracing the history on some mature topics and areas, others focusing on newly emerging areas, with forecasts into the future.
D.V. Mayne, the second author the textbook [RM15], published a survey paper in December 2014.
[Mayne14] D.Q. Mayne, "Model predictive control: Recent developments and future promise," Automatica, 50(12), December 2014, pp. 2967-2986.