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Many correct-by-construction control synthesis methods suffer from the curseof dimensionality. Motivated by this challenge, we seek to reduce acorrect-by-construction control synthesis problem to subproblems of more modestdimension. As a step towards this goal, in this paper we consider the problemof synthesizing decoupled robustly controlled invariant sets for dynamicallycoupled linear subsystems with state and input constraints. Our approach, whichgives sufficient conditions for decoupled invariance, is based on optimizationover linear matrix inequalities which are obtained using slack variableidentities. We illustrate the applicability of our method on several examples,including one where we solve local control synthesis problems in acompositional manner.

Synthesis of separable controlled invariant sets for modular local control design