Chapter 74, The Control Handbook, 2nd Edition, W. Levine (editor), CRC Press Inc., 2011.

This chapter gives an overview of results on finding algebraic conditions that allow one to simplify decentralized control problems. It summarizes several of the main results without giving any proofs, and could be a good first stop for those with a new interest in the topic. Much of it focuses on quadratic invariance, the condition which allows the optimal linear decentralized control problem to be recast as a convex optimization problem, including the results that one gets when applying quadratic invariance to control over networks. It also discusses a condition that allows for a similar parameterization of stabilizing nonlinear controllers, as well as results on how the optimal control problem can be transformed when these conditions do not hold.

This edition of the Handbook was released in a 3-volume set, with this chapter appearing in the volume on Control System Advanced Methods.