The thesis contributes to analyzing consensus robustness and performance problems of linear time-invariant (LTI) multi-agent systems subject to uncertain delays.

The thesis first investigates the first-order multi-agent systems with respect to uncertain gain and phase variations within a certain range. We consider dynamic output feedback control protocols in the form of proportional-integral (PI) control. Undirected communication graphs are considered. Firstly, we find that both the gain consensus margin and phase consensus margin are independent of agent dynamics and network topology for minimum phase systems. Moreover, for the nonminimum phase agents over undirected graphs, we compute the gain consensus margin and phase consensus margin analytically by solving two maximization problems, that is, some parametric max-min problems. The results show how the agent's unstable poles and nonminimum phase zeros, as well as the network topology may confine the gain and phase variation ranges so that consensus can or cannot be maintained.

Next, we demonstrate the best achievable consensus performance by state feedback protocol, whereas the performance quantifies the error in achieving consensus, under the disruption of noises and disturbances. Directed graphs are mainly considered. The H₂ and H_∞ norms of the transfer function are employed as measures of consensus error. Firstly, for H₂ consensus performance, the explicit expressions of the fundamental limits were already known. With regard to H_∞ consensus performance, we find the fundamental limit by solving a sequence of independent unimodal quasi-convex problems. In an additional effort, we examine the optimization problems of the network by incorporating key graph constraints. Our results demonstrate that appropriately distributing the graph Laplacian eigenvalues and edge weights optimizes the network, leading to improved consensus performance.

Finally, we first consider first-order continuous-time multi-agent systems and the dynamics agents controlled by output feedback protocol over undirected and directed graphs. The main objective is to determine the delay consensus margin and consensus performance which are achievable by consensus feedback protocol. Of equal importance as the gain consensus margin and the phase consensus margin, the delay consensus margin is a robustness measure as well which quantifies the largest delay range despite the variation and uncertainty of delay. Analytical expressions are obtained for both delay consensus margin and optimal consensus error performances, both of which shed useful light on limitations imposed by the agent dynamics and network topology on the robustness and performance of first-order multi-agent systems. For the directed graphs, we develop computational results and analytical bounds.

All the results presented in the thesis not only demonstrate the solvability of consensus robustness problems but also provide fundamental performance limits from the perspectives of H₂ and H_∞ norms, establishing some useful guidelines in the analytical design of feedback control.