Affine Controller Parameterization for Decentralized Control over Banach Spaces
- M. Rotkowitz and S. Lall.
- IEEE Transactions on Automatic Control, V. 51, No. 9, p. 1497--1500, 2006.
We cast the problem of optimal decentralized control as one of minimizing a closed-loop norm subject to a subspace constraint on the controller. In this note we consider continuous linear operators on Banach spaces, and show that a simple property called quadratic invariance is necessary and sufficient for the constraint set to be preserved under feedback, and thus allows optimal synthesis to be recast as a convex optimization problem. These results hold for any norm and any Banach space.