The available minimum variance (MV) benchmarks do not
take the
controller structure into account and thus can lead to incorrect conclusions
regarding the performance of decentralized controllers. In this paper,
we present a method for computing a lower bound on the least output
variance achievable using decentralized controllers, where the nonconvexity
of the optimization problem is handled using sums of squares programming.
Though tight, the computation of this lower bound requires that the
process model be known. As a more practical approach, we derive an
MV benchmark for performance assessment of decentralized controllers
on a loop by loop basis. The MV benchmark for loop by loop analysis
can be estimated from the closed loop operating data with the knowledge
of time delays between all the inputs and outputs. The usefulness
of the proposed benchmarks is demonstrated using simulation examples.