Network systems model natural and engineered processes composed of groups of physical components that interact with the environment, and that are coupled with each other by means of an intricate communication network. Network systems have been widely adopted to model and understand many complex physical processes, ranging from stock markets in economics, transportation networks in engineering, to evolutionary processes in biology. A fundamental property of these systems is their robustness to contingencies, that is, the capability of operating effectively despite external perturbations, such as accidental component failures, malicious targeted attacks, or external disturbances. In this dissertation, we address four engineering problems concerning robustness in network systems.

First, we study robustness in highway transportation systems where travelers follow routing suggestions provided by modern navigation apps (such as GoogleMaps, Waze, Inrix, etc.). Navigation apps provide minimum-time routing directions to the travelers based on global and instantaneous congestion information, thus transforming the way users behave and impacting the aggregate system behavior. We propose and analyze new models to capture the routing decisions of app-informed travelers that are inspired from selection and learning mechanisms in biology. Our analysis and techniques are rigorous, and can be applied to any traffic network topology, independently of its size or interconnection patterns. Our findings demonstrate that among numerous favorable benefits, routing apps can introduce new undesirable congestion phenomena, and that appropriate information design will be necessary to ensure the robustness of modern traffic infrastructures. Second, we propose a set of robust control algorithms to optimize the operation of the signalized traffic intersections in an urban traffic network in order to guarantee system-level optimality. Our methods are computationally-tractable, outperform state-of-the-art intersection control policies, and are effective to reduce congestion in major cities, as demonstrated by our simulations for Manhattan, NY. Third, with a focus on networks with linear dynamics, we develop theories and tools to study the robustness of a network against changes in the the communication links. Our methods include both rigorous algebraic conditions and tractable numerical algorithms, and ultimately relate the robustness of a system to the graph-theoretical properties of the underlying network interconnection. Fourth, with an application focus to robotics, we tackle the problem of ensuring robust navigation despite maliciously-compromised localization sensors. Our methods rely on the nonlinear notion of zero dynamics, and unveil fundamental limitations for attack detection. More generally, our results demonstrate for the first time that the choice of inputs adopted for control affects the security of a dynamical system.