Proceedings of the International Symposium on Mathematical Theory of Networks and Systems, July 2006.

The problem of finding an optimal decentralized controller is considered, where both the plant and the controllers under consideration are rational. It has been shown that a condition called quadratic invariance, which relates the plant and the constraints imposed on the desired controller, allows the optimal decentralized control problem to be cast as a convex optimaization problem, provided that a controller is given which is both stable and stabilizing. This paper shows how, even when such a controller is not provided, the optimal decentralized control problem may still be cast as a convex optimization problem, albeit a more complicated one. The solution of the resulting convex problem is then discussed.

The result that quadratic invariance gives convexity is thus extended to all finite-dimensional linear problems. In particular, this result may now be used for plants which are not strongly stablizable, or for which a stabilizing controller is simply difficult to find. The results hold in continuous-time or discrete-time.