The problem of parameterizing all stabilizing controllers subject to constraints is considered. A new condition relating the plant and the constraints is introduced, and it is shown that when it holds, the constraints are invariant under feedback.
There is no assumption of linearity or time-invariance on either the plant or the admissible controllers, only causality. There is also no assumption that the constraint set be a subspace, only that it is closed. The results hold in continuous time or discrete time.
When the condition holds, we then obtain a parameterization of all stabilizing controllers subject to the specified constraints, which is a convex parameterization as long as the desired constraint set is convex.