On the robustness of networked cooperative tracking systems

This paper provides an analytical framework for the robustness of networked multi-agent systems (MAS). It is well-known that a single-agent linear quadratic regulator (LQR) system can guarantee 60° phase margin and infinite gain margin. However, for networked MAS, there exist no theoretical results on guaranteed stability margins, due to the complexity caused by the interplay of communication structure and agents’ dynamics. In this paper, we analyze the effect of communication graph topology on the robustness properties of networked cooperative tracking systems with local LQR designs. For such systems, we provide closed-form expressions of phase and gain margins modulated by their graph topology, following a Lyapunov type of analysis. We further derive upper bounds of stability margins for MAS with general graph topology, through a structural analysis based on the algebraic graph theory. We prove that the directed tree communication topology is among the most robust graph topology that promises the best stability margins, which are as good as the ones in a single-agent LQR system