A State Space Analysis of the Stability and Robustness Properties of Model Predictive Control (MPC)

By using known closed-form, matrix expressions for the optimal gain with Model Predictive Control (MPC), and by using a state space model for prediction, the input/output closed loop MPC system is cast into a standard closed loop state space form. Then standard conditions for stability may be derived from the eigenvalues of the equivalent closed loop plant matrix being all less than unity in magnitude. Preliminary discussions also relate these rsults to selection of the numerous design parameters of MPC to optimize robustness.