State Feedback System Level Synthesis in Continuous Time

Abstract: System level synthesis (SLS) is a controller parameterization technique that facilitates synthesis of structured distributed controllers via convex optimization. Past results on SLS are primarily in the discrete-time setting; this paper extends SLS to the continuous-time setting. We translate the parametrization and associated constraints to continuous-time, and propose a controller design procedure consisting of two steps: (1) selection of poles and (2) optimization over closed-loop responses. We provide SLS parameterizations for continuous-time $\H2$ and $\Hinf$ control, and show that the proposed procedure allows us to design structured $\H2$ and $\Hinf$ controllers via convex optimization. Furthermore, the proposed procedure preserves the scalability and local-disturbance-rejection features of the original discrete-time SLS framework. We verify our findings in simulation -- on a grid of 9 nodes governed by linearized swing equations, our structured distributed controllers perform similarly to the optimal centralized controllers.