The main interest of the present thesis is the constrained control of time-delay system, more specifically taking into consideration the discretization problem (due to, for example, a communication network) and the presence of constraints in the system's trajectories and control inputs. The effects of data-sampling and modeling problem are studied in detail, where an uncertainty is added into the system due to additional effect of the discretization and delay. The delay variation with respect to the sampling instants is characterized by a polytopic supra-approximation of the discretization/delay induced uncertainty. Some stabilizing techniques, based on Lyapunov's theory, are then derived for the unconstrained case. Lyapunov-Krasovskii candidates were also used to obtain LMI conditions for a state feedback, in the ''original" state-space of the system. For the constrained control purposes, the set invariance theory is used intensively, in order to obtain a region where the system is ''well-behaviored", despite the presence of constraints and (time-varying) delay. Due to the high complexity of the maximal delayed state admissible set obtained in the augmented state-space approach, in the present manuscript we proposed the concept of set invariance in the ''original" state-space of the system, called D-invariance. Finally, in the las part of the thesis, the MPC scheme is presented, in order to take into account the constraints and the optimality of the control solution.

[pt] Esta dissertação apresenta uma comparação entre técnicas de discretização de controladores, considerando diferentes estruturas de controle. Os tipos de sistemas estudados neste trabalho de pesquisa serão sistemas lineares, invariantes no tempo, determinísticos, causais e monovariáveis. O desempenho das técnicas de discretização serão comparados via figuras de mérito tradicionais, considerando os métodos de discretização, as estruturas dos controladores e os tipos de planta habituais (incluindo problemas benchmarch), sob especificações dadas quanto aos regimes permanente e transiente. / [en] This essay proposes a comparison between techniques of controllers´ discretization considering different controlling structures. The types of systems studied in this research will be linear systems, time-invariant, deterministic, casual and single-variable. The performance of discretization techniques will be compared through figures of traditional aptitude, considering the discretization methods, the controller structures and the kinds of plants (including - benchmarch - problems), under given specifications according to permanent and transitory systems. / [es] Esta disertación presenta una comparación entre técnicas de discretización de controladores, considerando diferentes extructuras de control. Los tipos de sistemas estudiados en este trabajo de investigación son sistemas lineales, invariantes en el tiempo, determinísticos, causales y univariados. Se compara el desempeño de las técnicas de discretización utilizando figuras de mérito tradicionales, considerando los métodos de discretización, las extructuras de los controladores y los tipos de planta habituales (incluyendo problemas - benchmarch - ), bajo especificaciones dadasen relación a los régimenes permanente y transiente.

Le thème principal de ce mémoire est la commande sous contraintes pour des systèmes à retard, en tenant compte de la problématique d’échantillonnage (où les informations concernant le système en temps continu sont, par exemple, envoyées par un réseau de communication) et de la présence de contraintes sur les trajectoires du système et sur l’entrée de commande. Pendant le processus d’échantillonnage, le retard variable dans le temps peut être traité comme une incertitude, le but étant de confiner cette variation dans un polytope, de façon à couvrir toutes les variations possibles du retard. Pour stabiliser des systèmes à retard, nous nous sommes basés sur la théorie de Lyapunov. En utilisant cette méthode, nous pouvons trouver un retour d’état qui stabilise le système malgré la présence du retard variable dans la boucle. Une autre possibilité est l’utilisation des candidates de Lyapunov-Krasovskii. La théorie des ensembles invariants est largement utilisée dans ce manuscrit, car il est souhaitable d’obtenir une région de ≪ sûreté ≫, ou le comportement du système est connu, en dépit de la présence du retard (variable) et des contraintes sur les trajectoires du système. Lorsqu’ils sont obtenus dans l’espace d’état augmenté, les ensembles invariants sont très complexes, car la dimension de l’espace Euclidien sera proportionnelle à la taille du système mais aussi à la taille du retard. Le concept de D-invariance est ainsi proposé. La commande prédictive (en anglais MPC) est présentée, pour tenir compte des contraintes sur les trajectoires et appliquer une commande optimale à l’entrée du système. / The main interest of the present thesis is the constrained control of time-delay system, more specifically taking into consideration the discretization problem (due to, for example, a communication network) and the presence of constraints in the system’s trajectories and control inputs. The effects of data-sampling and modeling problem are studied in detail, where an uncertainty is added into the system due to additional effect of the discretization and delay. The delay variation with respect to the sampling instants is characterized by a polytopic supra-approximation of the discretization/delay induced uncertainty. Some stabilizing techniques, based on Lyapunov’s theory, are then derived for the unconstrained case. Lyapunov-Krasovskii candidates were also used to obtain LMI conditions for a state feedback, in the ``original” state-space of the system. For the constrained control purposes, the set invariance theory is used intensively, in order to obtain a region where the system is ``well-behaviored”, despite the presence of constraints and (time-varying) delay. Due to the high complexity of the maximal delayed state admissible set obtained in the augmented state-space approach, in the present manuscript we proposed the concept of set invariance in the ``original” state-space of the system, called D-invariance. Finally, in the las part of the thesis, the MPC scheme is presented, in order to take into account the constraints and the optimality of the control solution.