Decentralized Control of Unstable Systems and Quadratically Invariant Information Constraints

We consider the problem of constructing decentralized control systems for unstable plants. We formulate this problem as one of minimizing the closed-loop norm of a feedback system subject to constraints on the controller structure, and explore which problems are amenable to convex synthesis. For stable systems, it is known that a property called quadratic invariance of the constraint set is important. If the constraint set is quadratically invariant, then the constrained minimum-norm problem may be solved via convex programming. Examples where constraints are quadratically invariant include many classes of sparsity constraints, as well as symmetric constraints. In this paper we extend this approach to the unstable case, allowing convex synthesis of stabilizing controllers subject to quadratically invariant constraints.