Robust synchronisation of heterogeneous networks via integral quadratic constraints

A general framework for the study of robust synchronisation in large-scale networks is provided. Agents are represented as a common nominal linear time-invariant (LTI) single-input-single-output (SISO) system with simple poles on the imaginary axis, subject to LTI SISO stable multiplicative perturbations. The agents exchange information in order to achieve output-synchronisation, namely steer their outputs to the same, possibly time-varying, signal. Such an information exchange is modeled through a sparse dynamical operator that maps the outputs of the agents into their inputs. The theory of integral quadratic constraints is used to capture the structural uncertainties of the perturbations, and to give certificates for robust synchronisation of the systems. Since the IQC theory is nominally applied to open-loop stable systems, the main idea is to introduce a new space of signals with respect to which the notion of feedback stability implies that of synchronisation under appropriate assumptions on the interconnection operator. The proposed criterion unifies and extends several results in the literature.