A fault in the system operation is deemed to occur when the system practically experiences an abnormal condition, such as a malfunction in the actuators/sensors. Hence, detection and isolation of the faulty components is crucial in control applications. Effective control and monitoring of a system requires accurate information of internal behaviour of the system. This internal behaviour can be analyzed by system's states. Practically, in many real systems, state space variables are not fully available for measurements. The two critical problems stated have motivated significant research work in the area of robust state and fault estimation. Fault reconstruction and estimation is regarded as a stronger extension to fault detection and isolation (FDI) since accurate fault estimation automatically implies fault detection. It is well known that two promising control strategies to cope with uncertain control processes are H_infinity Control and Sliding Mode Control. Therefore, in this PhD thesis, we employ these tools and we propose observer based robust fault reconstruction (RFR) by integrating H_infinity filtering and Sliding Mode Control. We also employ adaptive control on the sliding motion to deal with faults with unknown bounds. Another open problem in the context of FDI and RFR is due to systems with multiple faults at different system's components since it is often the case where actuators and also sensors suffer from faults during the course of the system's operation. Both actuators and sensors can suffer from faults either alone, at separate times or simultaneously. The co-existence of unknown fault at both sensor(s) and actuator(s) has not been addressed in any earlier design of fault reconstruction schemes. In this Thesis, inspired by the theory of singular systems, we aim at solving this problem. A New structure for reduced-order unknown input observers (UIOs) with application to chaotic communication and sensor fault reconstruction is also proposed. / Controls

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L’analyse et la synthèse des systèmes dynamiques ont connu un développement important au cours des dernières décennies comme l’atteste le nombre considérable des travaux publiés dans ce domaine, et continuent d’être un axe de recherche régulièrement exploré. Si la plupart des travaux concernent les systèmes linéaires et non linéaires temps continu, peu de résultats ont étaient établis dans le cas temps discret. Les travaux de cette thèse portent sur l’observation et la commande d’une classe de systèmes non linéaires à temps discret. Dans un premier temps, le problème de synthèse d’observateur d’état utilisant une fenêtre de mesures glissante est abordé. Des conditions de stabilité et de robustesse moins restrictives sont déduites. Deux classes de systèmes non linéaires à temps discret sont étudiées : les systèmes de type Lipschitz et les systèmes « one-sided Lipschitz ». Ensuite, une approche duale a été explorée afin de déduire une loi de commande stabilisante basée sur un observateur. Les conditions d’existence d’un observateur et d’un contrôleur stabilisant les systèmes étudiés sont formulées sous forme d’un problème d’optimisation LMI. L’efficacité et la validité des approches présentées sont montrées à travers des exemples académiques / The analysis and synthesis of dynamic systems has undergone significant development in recent decades, as illustrated by the considerable number of published works in this field, and continue to be a research theme regularly explored. While most of the existing work concerns linear and nonlinear continuous-time systems, few results have been established in the discrete-time case. This thesis deals with the observation and control of a class of nonlinear discrete-time systems. First, the problem of state observer synthesis using a sliding window of measurements is discussed. Non-restrictive stability and robustness conditions are deduced. Two classes of discrete time nonlinear systems are studied: Lipschitz systems and one-side Lipschitz systems. Then, a dual approach was explored to derive a stabilizing control law based on observer-based state feedback. The conditions for the existence of an observer and a controller stabilizing the studied classes of nonlinear systems are expressed in term of LMI. The effectiveness and validity of the proposed approaches are shown through numerical examples