Distributed robustness analysis of heterogenous networks via integral quadratic constraints

Integral Quadratic Constraints (IQC) are known as a versatile tool for characterising dynamic behaviours in a form that facilitates robustness analysis of feedback systems within a unifying framework. Numerous model uncertainties can be described by IQC, such as disturbances with bounded frequency content and the nonlinear effects of hysteresis. This talk first extends the classical IQC theory for feedback to tackling the problem of synchronising multiple linear time-invariant agents in a network, where additional efforts are required to handle the marginally stable dynamics present in the setup. Distributed synchronisation certificates are proposed and shown to specialise to certain results in the literature. Subsequently for large-scale interconnected nonlinear systems, we will discuss a method to improve the computational scalability of IQC analysis based on the notion of sparse decomposition of sign definite matrices. This opens up the possibility to verify robust stability and performance of large-scale networks in a distributed fashion that scales well with the addition/removal of agents.