# Constrained control for time-delay systems.

Abstract : 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.
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Cited literature [191 references]

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### File

Thesis_LOMBARDI.pdf
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### Identifiers

• HAL Id : tel-00631507, version 2

### Citation

Warody Lombardi. Constrained control for time-delay systems.. Other. Supélec, 2011. English. ⟨NNT : 2011SUPL0010⟩. ⟨tel-00631507v2⟩

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