Necessary and sufficient conditions for stabilizablity in decentralized control and estimation
This talk is centered on necessary and sufficient conditions for the existence of solutions to two problems concerning the stabilizability of decentralized systems. The first is the design of a stabilizing controller subject to pre-selected quadratically invariant sparsity constraints (as defined by Rotkowitz and Lall). We show that the stabilizability problem can be cast as the existence of solutions to a classical exact model-matching problem, which can be tackled using existing techniques. This result leads to a new convex parametrization of all stabilizing sparsity-constrained controllers that, unlike existing techniques, does not rely on an initial guess. Our approach is the first sparsity-constrained counterpart to Youlas classical parametrization. (This work is in collaboration with Dr. Serban Sabau).
The second part of the talk will focus on the design of distributed observers. Here we consider a collection of LTI observers that are connected according to a pre-specified graph, and where each has access to a sub-partition of the output of an LTI plant. The objective is to design the observers to achieve asymptotic omniscience of state of the plant, i.e., the estimate at each observer must converge to the state of the plant. We provide necessary and sufficient conditions for the existence of such observers. Our method is constructive and is rooted on the analysis of the fixed modes of an associated feedback system. Unlike existing results, the fact that our distributed observers are LTI facilitates the use of frequency domain methods for performance analysis in the presence of noise. (This work is in collaboration with Mr. Shinkyu Park)