Optimal decentralized control of linear systems via Groebner bases and variable elimination

We consider the problem of optimal decentralized controller synthesis. There are several classes of such problems for which effective algorithms are known, including the quadratically invariant cases. In this paper, we use Groebner bases and elimination methods to characterize all the possible closed-loop maps which are obtainable by forming a feedback loop with decentralized controllers. We show that this approach allows solution of a strictly wider class of optimal decentralized control problems than the quadratically invariant ones.