Stable MPC with reduced representation for linear systems with multiple input delays

It is well known that MPC recursive feasibility and asymptotic stability is related to the so called stabilizing elements, namely: (i) terminal cost, (ii) terminal stabilizing control law, and terminal constraint. For systems with multiple delays, it is commonly used an augmented representation, which avoid the use of input delays. However, although the augmented description permits an easy inclusion of the stabilizing elements, the control problem dimension could be prohibitively enlarged (mainly from a computational point of view). In this paper it is shown that a stable MPC with enlarged domain of attraction can be easily applied to control open-loop stable systems with multiple input delays by considering the original (reduced) representation. Stabilizing conditions are presented and a modified cost function is proposed in order to avoid the augmented representation. A simulation example is presented to illustrate the simplicity of the proposed approach.