M. Rotkowitz and S. Lall
On Computation of Optimal Controllers Subject to Quadratically Invariant Sparsity Constraints
Proceedings of the American Control Conference, pp. 5659-5664, June 2004.

Abstract

We consider the problem of constructing optimal sparse controllers. It is known that a property called quadratic invariance of the constraint set is important, and results in the constrained minimum-norm problem being soluble via convex programming. We provide an explicit method of computing $Htwo$-optimal controllers subject to quadratically invariant sparsity constraints, along with a computational test for quadratic invariance. As a consequence, we show that block diagonal constraints are never quadratically invariant unless the plant is block diagonal as well.