Convex robust performance with structured uncertainties in System Level Synthesis

We develop convex parameterizations for ℒ
1
-robust controllers in the System Level Synthesis (SLS) framework, allowing us to find robust decentralized controllers that preserve design constraints on sparsity, locality, and delay. The parameterizations have interpretable relationships with the set of nominally stabilizing SLS controllers. We show that the state feedback robust performance SLS problem can be posed exactly and end-to-end as a linear program applicable to large-scale distributed control. We generalize these results to unstructured uncertainties in the output feedback setting, providing new decentralized robust performance guarantees in this setting.