MIMO Networks with Heterogeneous Uncertainties: Topology-Independent Robust Stability and α-Convergence

We consider network systems where the node dynamics are described by identical MIMO LTI subsystems with transfer-function matrix F(s), while the dynamic interactions associated with the bidirectional arcs are described by identical MIMO LTI subsystems with transfer-function matrix G(s); the dynamics of the individual nodes and arcs are affected by heterogeneous, norm-bounded uncertainties. We provide a topology-independent condition for the robust stability of all possible network systems with a maximum connectivity degree, regardless of their size and interconnection structure. We also give a topology-independent condition that robustly guarantees not only stability, but also α-convergence (i.e. all poles having real part less than a negative - α). The proposed frequency-domain conditions are scalable and can be evaluated locally, also for large-scale networks where nodes and arcs can be added or removed in real time. The conditions are applied to assess the robust α-convergence of a suspension bridge system of arbitrary size.