Robustness and Performance Analysis of Cyclic Interconnected Dynamical Networks

The class of cyclic interconnected dynamical networks plays a crucial role in modeling of certain biochemical reaction networks. In this paper, we consider cyclic dynamical networks with loop topology and quantify bounds on various performance measures. First, we consider robustness of autonomous cyclic dynamical networks with respect to external stochastic disturbances. The H2–norm of the system is used as a robustness index to measure the expected steadystate dispersion of the state of the entire network. In particular, we explicitly quantify how the robustness index depends on the properties of the underlying digraph of a cyclic network. Next, we consider a class of cyclic dynamical networks with control inputs. Examples of such cyclic networks include a class of interconnected dynamical networks with some specific autocatalytic structure, e.g., glycolysis pathway. We characterize fundamental limits on the ideal performance of such cyclic networks by obtaining lower bounds on the minimum L2–gain disturbance attenuation. We show that how emergence of such fundamental limits result in essential tradeoffs between robustness and efficiency in cyclic networks.