### Abstract

This paper presents a novel method for designing the terminal cost and the auxiliary control law (ACL) for robust MPC of uncertain linear systems, such that ISS is a priori guaranteed for the closed-loop system. The method is based on the solution of a set of LMIs. An explicit relation is established between the proposed method and H_infty control design. This relation shows that the LMI-based optimal solution of the H_infty synthesis problem solves the terminal cost and ACL problem in inf-sup MPC, for a particular choice of the stage cost. This result, which was somehow missing in the MPC literature, is of general interest as it connects well known linear control problems to robust MPC design.

Original language | English |
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Title of host publication | Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia |

Pages | 1-8 |

Publication status | Published - 2008 |

Event | 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08) - Pavia, Italy Duration: 5 Sep 2008 → 9 Sep 2008 Conference number: 3 |

### Workshop

Workshop | 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control (NMPC08) |
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Abbreviated title | NMPC08 |

Country | Italy |

City | Pavia |

Period | 5/09/08 → 9/09/08 |

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## Cite this

Lazar, M., Heemels, W. P. M. H., Munoz de la Pena, D., & Alamo, T. (2008). Further results on "Robust MPC using Linear Matrix Inequalities". In

*Proceedings of the 3rd International Workshop on Assessment and Future Directions of Nonlinear Model Predictive Control, 5-9 September 2008, Pavia, Italia*(pp. 1-8)