The comprehensive integration of instrumentation, communication, and control into physical systems has led to the study of Cyber-Physical Systems (CPS), a field that has recently garnered increased attention. A key concern that is ubiquitous in CPS is a need to ensure security in the face of cyber attacks. In this paper, we carry out a survey of systems and control methods that have been proposed for the security of CPS. We classify these methods into three categories based on the type of defense proposed against the cyberattacks: prevention, resilience, and detection & isolation. A unified threat assessment metric is proposed in order to evaluate how CPS security is achieved in each of these three cases. Also surveyed are risk assessment tools and the effect of network topology on CPS security. An emphasis has been placed on power and transportation applications in the overall survey. Index Terms-cyber-physical systems, resilient control I. INTRODUCTION Motivated by concerns about sustainability, efficiency, and resiliency, several sectors including energy, transportation, water, and healthcare systems have witnessed significant advances in instrumentation, monitoring, and automation over the past decade. The resulting integration of information, communication, and computation with physically engineered systems demands a detailed investigation into the analysis and synthesis of Cyber-Physical Systems (CPS) so as to realize the desired performance metrics of efficiency, sustainability, and safety. The extensive and intricate presence of cyber components also introduces a vulnerability of unwanted access to these systems. The available communication technologies, referred to as SCADA (Supervisory Control and Data Acquisition), are witnessing significant advances, triggering a shift from protected, closed, and wired networks to open and wireless networks which, as a side effect, are more vulnerable to outside interference.

We provide bounds on the smallest eigenvalue of grounded Laplacian matrices (which are obtained by removing certain rows and columns of the Laplacian matrix of a given graph). The gap between our upper and lower bounds depends on the ratio of the smallest and largest components of the eigenvector corresponding to the smallest eigenvalue of the grounded Laplacian. We provide a graph-theoretic bound on this ratio, and subsequently obtain a tight characterization of the smallest eigenvalue for certain classes of graphs. Specifically, for Erdos-Renyi random graphs, we show that when a (sufficiently small) set S of rows and columns is removed from the Laplacian, and the probability p of adding an edge is sufficiently large, the smallest eigenvalue of the grounded Laplacian asymptotically almost surely approaches |S|p.We also show that for random d-regular graphs with a single row and column removed, the smallest eigenvalue is Θ( d n ). Our bounds have applications to the study of the convergence rate in consensus dynamics with stubborn or leader nodes.

We study linear consensus and opinion dynamics in networks that contain stubborn agents. Previous work has shown that the convergence rate of such dynamics is given by the smallest eigenvalue of the grounded Laplacian induced by the stubborn agents. Building on this, we define a notion of centrality for each node in the network based upon the smallest eigenvalue obtained by removing that node from the network. We show that this centrality can deviate from other well known centralities. We then characterize certain properties of the smallest eigenvalue and corresponding eigenvector of the grounded Laplacian in terms of the graph structure and the expected absorption time of a random walk on the graph.

As bulk synchronous generators in the power grid are replaced by distributed generation interfaced through power electronics, inertia is removed from the system, prompting concerns over grid stability.Different metrics are available for quantifying grid stability and performance; however, no theoretical results are available comparing and contrasting these metrics. This paper presents a rigorous systemtheoretic study of performance metrics for low-inertia stability. For networks with uniform parameters, we derive explicit expressions for the eigenvalue damping ratios, and for the H 2 and H ∞ norms of the linearized swing dynamics, from external power disturbances to different phase/frequency performance outputs.These expressions show the dependence of system performance on inertia constants, damping constants, and on the grid topology. Surprisingly, we find that the H 2 and H ∞ norms can display contradictory behavior as functions of the system inertia, indicating that low-inertia performance depends strongly on the chosen performance metric.

We present a graph-theoretic approach to analyzing the robustness of leader-follower consensus dynamics to disturbances and time delays. Robustness to disturbances is captured via the system H 2 and H ∞ norms and robustness to time delay is defined as the maximum allowable delay for the system to remain asymptotically stable. Our analysis is built on understanding certain spectral properties of the grounded Laplacian matrix that play a key role in such dynamics. Specifically, we give graph-theoretic bounds on the extreme eigenvalues of the grounded Laplacian matrix which quantify the impact of disturbances and time-delays on the leader-follower dynamics. We then provide tight characterizations of these robustness metrics in Erdos-Renyi random graphs and random regular graphs. Finally, we view robustness to disturbances and time delay as network centrality metrics, and provide conditions under which a leader in a network optimizes each robustness objective. Furthermore, we propose a sufficient condition under which a single leader optimizes both robustness objectives simultaneously.