Scalable stability conditions for heterogeneous networks via integral quadratic constraints

Decentralised and scalable conditions for robust stability of networks of heterogenous linear time-invariant (LTI) systems are derived based on integral quadratic constraints. These generalise previous works in the literature with an increased flexibility in the choice of multipliers employed. The results allow for arbitrary interconnection matrices and accommodate multi-input-multi-output systems. Similar conditions are also developed for nonlinear systems interconnected with LTI systems following a bipartite structure. In particular, the stability certificates only involve each individual LTI agent and its nearest nonlinear neighbours