Eigenvalue properties of discrete time linear receding horizon control systems

The paper deals with the stability properties of discrete time linear model predictive control systems. The closed loop systems are optimized using different performance criterions in a receding horizon fashion, and then the eigenvalue properties of the closed loop systems are investigated for the different conditions. Performance criterions may be combinations of terms belonging to state, control and state error at the horizon end. Eigenvalue properties of each class of cost functions depending on the horizon length are elaborated based on some new control theoretical results. Behaviors of receding horizon control algorithms are presented on a classical control problem, the stabilization of the inverted pendulum around the upper unstable equilibrium