Internal Quadratic Invariance and Decentralized Control

For decentralized control systems with quadratically invariant information constraints, the set of achievable closed-loop maps is affine, and thus the associated minimum-norm controller synthesis problem is amenable to a convex programming approach. In this paper, we show that a strictly broader class of problems we call internally quadratically invariant, also yields an affine set of achievable closed-loop maps. We treat systems represented by rational as well as proper rational transfer functions and present an illustrative example.