Structured state space realizations for SLS distributed controllers

In recent work the system level synthesis (SLS) paradigm has been shown to provide a truly scalable method for synthesizing distributed feedback controllers. Moreover, the resulting synthesis problem is convex. In this paper we provide minimal state space realizations for both the state and output feedback controllers. It is also shown that (for fixed n) the state dimension of the controllers grows linearly with FIR filter horizon length — in both cases, we show that if the underlying transfer matrices are structured, so is the corresponding state-space realization. For the H2 state feedback case a simple decomposition technique reduces the synthesis problem to solving a set of lower dimensional LQR problems that can be solved in parallel.

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