The original MPC(Model Predictive Control) algorithm cannot be applied to open loop unstable systems, because the step responses of the open loop unstable system never reach steady states. So when we apply MPC to the open loop unstable systems, first we have to stabilize them by state feedback or output feedback. Then the stabilized systems can be controlled by MPC. But problems such as valve saturation may occur because the manipulated input is the summation of the state feedback output and the MPC output. Therefore, we propose Quadratic Dynamic Matrix Control(QDMC) combined with state feedback as a new method to handle the constraints on manipulated variables for multivariable unstable processes. We applied this control method to a single-input-single-output unstable nonlinear system and a multi-input- multi-output unstable system. The results show that this method is robust and can handle the input constraints explicitly and also its control performance is better than that of others such as well tuned PI control, Linear Quadratic Regulator (LQR) with integral action.

Astrom KJ, Wittenmark B, "Computer Controlled System: Theory and Design," Prentice-Hall (1984)
Cheng CM, Ind. Eng. Chem. Res., 28, 178 (1989) 
Cutler CR, Ph.D. Thesis, U. of Houston (1983)
Cutler CR, ISA Trans., 21, 1 (1982)
Cutler CR, Ramaker BL, "Dynamic Matrix Control-A Computer Control Algorithm," AIChE 86th National Meeting, Apr. (1979)
Deshpande PB, "Distillation Dynamics and Control," Instrument Society of America (1985)
Garcia CE, Morshedi AM, Chem. Eng. Commun., 46, 73 (1986)
Georgiou A, Georgakis C, Luyben WL, Ind. Eng. Chem. Res., 28, 1481 (1989) 
Hidalgo PM, Brosilow CB, Comput. Chem. Eng., 13, 481 (1990) 
Maurath PR, Laub AJ, Seborg DE, Mellichamp DA, Ind. Eng. Chem. Res., 27, 1204 (1988) 
Ogata K, "State Space Analysis of Control Systems," Prentice-Hall (1967)
Ray WH, "Advanced Process Control," McGraw-Hill (1981)