This thesis concerns stability analysis and robust H¡Û performance analysis for discrete-time systems with interval time-varying delay; moreover, the results are extended to the systems with norm-bounded uncertainties. By defining a novel Lyapunov functional and combining delay partition methods to improve the results in existing literature, we obtain a less conservative linear matrix inequality condition to guarantee the asymptotic stability for the discrete-time systems. There are examples to illustrate the advantage of our method in every chapter.

Networked haptic cooperation entails direct interactions among the networked users in addition to joint manipulations of shared virtual objects. For example, therapists may want to feel and guide the motions of their remote patients directly rather than via an intervening virtual object during tele-rehabilitation sessions. To support direct user-to-user haptic interaction over a network, this dissertation introduces the concept of remote dynamic proxies and integrates it into two distributed control architectures. The remote dynamic proxies are avatars of users at the sites of their distant peers. They have second order dynamics and their motion is coordinated to the remote user whom they represent either via virtual coupling or via wave-based control. The remote dynamic proxies render smooth motion of the distant peers regardless of the infrequent and delayed information received over the network. Therefore, the integration of remote dynamic proxies into distributed networked haptic cooperation allows stiffer contacts to be rendered to users and improves position coherency in the presence of longer constant network delays. The thesis investigates the advantages and limitations of the remote dynamic proxies for two distributed haptic architectures. These architectures coordinate the peer users and their virtual environments via: - virtual coupling control. For virtual coupling-based networked haptics with remote dynamic proxies, stability is analyzed within a multi-rate state space framework and the analysis is validated through experiments involving both cooperative manipulations and direct user-to-user interactions. The results show that the remote dynamic proxies maintain high coherency between the distributed virtual environments and enable users to see and feel their peers moving smoothly. They also increase the stiffness of direct user-to-user contact in the presence of larger constant network delay. However, the remote dynamic proxies do not lessen users' perception of a predominantly viscous virtual environment in the presence of network delay. - wave-based control. To enable users to feel other dynamics in addition to viscosity during networked haptic cooperation, this dissertation further develops a wave-based distributed coordination approach for the remote dynamic proxies. The performance of the proposed approach is investigated via experiments involving both cooperative manipulations and direct user-to-user interactions. The results demonstrate that the remote dynamic proxies mitigate the poor coherency typical to wave-based coordination architectures and enable users to touch their peers. Furthermore, the remote dynamic proxies improve users' perception of inertia in the presence of network delay.

Les interfaces haptiques à retour d’effort sont des dispositifs robotiques capables deproduire des forces à destination de l’utilisateur en téléopération et en réalité virtuelle. L’utilisation d’interface à retour d’effort en Conception Assistée par Ordinateur (CAO) offre de nouvelles perspectives pour la création et la conception de formes 3D grâce à une interactivité à la fois visuelle et kinesthésique. Elles permettent à la fois de visualiser, de manipuler en temps réel des objets virtuels et d’en ressentir les efforts (liés aux contacts, à la déformation, etc.).Les travaux présentés dans cette thèse contribuent au développement d’interfaces àretour d’effort pour répondre au mieux aux besoins de la CAO. Dans ce mémoire, l’accent est placé sur la problématique de la stabilité et son exploitation pour la commande de l’interface mais aussi pour la conception électromécanique. L’ensemble des travaux porte sur une interface à un degré de liberté.Dans un premier temps, différents facteurs liés au système mécanique (amortissement, modes vibratoires) et à l’environnement virtuel (échantillonnage, retard. . .) agissant sur la stabilité d’une interface sont mis en évidence à l’aide de critères fréquentiels. Ensuite, la conception d’une interface (choix et dimensionnement des composants) est ramenée sous forme d’un problème d’optimisation incluant une contrainte liée à la stabilité (en termes de domaine d’utilisation) et un critère de maximisation de la transparence (en termesd’inertie du dispositif).Dans un second temps, l’architecture de commande des dispositifs haptiques est étudiée. À l’aide d’une nouvelle condition de stabilité asymptotique pour les systèmes en temps discret à retard variable et en utilisant un observateur d’état augmenté comme alternative à l’utilisation standard de la méthode des différences finies arrières, la synthèse d’une nouvelle architecture de commande est proposée.La dernière partie du mémoire aborde la description du banc d’essai expérimental développé pendant le travail de thèse ainsi que les résultats des tests réalisés. / Force feedback haptic interfaces are robotic devices which are able to produce forces for the user in a teleoperation or virtual reality context. The integration of force feedback haptic interfaces in Computer-Aided Design (CAD) systems offers new perspectives for modeling and design of 3D objects by combining both visual and kinesthetic interaction. It allows viewing and manipulating virtual objects in real-time with a sense of touch (linked to contact, deformation, etc.).The works presented in this thesis contribute to the development of a force feedbackhaptic device to meet the needs of CAD at the best. In this thesis manuscript, the emphasis is put on the stability issue and its exploitation for the control of the device but also for the electromechanical conception. All the presented works concern an interface with one degree of freedom. First, several factors relative to the mechanic system (physical damping, vibration modes) and to the virtual environment (sampling period, delay-time, etc.) acting on the interface stability are highlighted through frequency domain stability criteria. Then, the interface design (choice and sizing of components) is expressed on the form of an optimization problem including a constraint linked to stability (in terms of application area).In a second part, the control architecture of haptic devices is studied. Using a newstability criterion for systems in discrete time with variable delay and an augmented state observer as an alternative to the standard finite difference scheme, the synthesis of novel control architecture is proposed.The last part of the manuscript deals with the description of the experimental testbench developed during the thesis period together with the results of some realized tests.