Distributed Control of Descriptor Networks: A Convex Procedure for Augmented Sparsity

For networks of systems, with possibly improper transfer function matrices, we present a design framework that enables
$\mathcal {H}_\infty$
control, while imposing sparsity constraints on the coprime factors of the controller. We propose a convex and iterative optimization procedure with guaranteed convergence to obtain distributed controllers. By exploiting the robustness-oriented nature of our proposed approach, we provide the means to obtain sparse representations of our control laws that may not be directly supported by the nominal model of the network.