Global stabilization of linear discrete-time systems with bounded controls-a model predictive control approach

Abstract

A linear discrete-time system is globally stabilizable with bounded controls if and only if the system is stabilizable and all its poles are in the closed unit disk. In this paper, the authors propose an implementable model predictive control algorithm to globally stabilize such systems. The authors show that with this scheme a linear discrete-time system with n poles on the unit disk (with any multiplicity) can be globally stabilized if the number of control moves is at least n+1. For pure integrating systems, this condition is also necessary. Moreover the authors show that global asymptotic stability is preserved for any asymptotically constant disturbance entering at the plant input.