Obtaining a Stabilizing Prediction Horizon in Quadratic Programming Model Predictive Control

In this paper, it is shown how a performance tuple can be obtained in model predictive control if the optimal control problem is a quadratic program. The quotient of the finite-horizon optimal cost and the tuple's first entry upper bounds the sum of all instances over the finite-horizon optimal cost. The tuple's second entry is a stabilizing prediction horizon. The algorithm taking the describing matrices and giving a performance tuple is easily verifiable.