An Explicit Parametrization of Closed Loops for Spatially Distributed Controllers With Sparsity Constraints

In this article,we study the linear time-invariant state-feedback controller design problem for distributed systems. We follow recently developed system level synthesis (SLS) approach and impose locality structure on resulting closed-loop mappings; corresponding implementation inherits prescribed structure. contrast to existing SLS results, we derive an explicit (rather than implicit) parameterization of all achievable stabilized closed-loops. This admits more efficient IIR representations temporal part dynamics, it allows $\mathcal {H}_2$ with spatial sparsity constraints be converted a standard model matching problem, number transfer function parameters scaling linearly extent constraint. illustrate our results two applications: consensus first-order subsystems vehicular platoons problem. case consensus, provide analytic solutions further analyze architecture implementation. Results infinite spatially invariant systems are presented insight large but finite subsystems.