That sounds about right. The extra thing that they are claiming is that these assumptions are things that naturally apply in real life, when a controller is doing its job (ie. they are not just contrived/​chosen to get the result). So (Wonham et al claim) the interesting thing is that you can say that these isomorphisms hold in actual systems. Obviously there are a bunch of issues with this. I intentionally avoided too much discussion and criticism in this post and put it in a separate post.
That sounds about right. The extra thing that they are claiming is that these assumptions are things that naturally apply in real life, when a controller is doing its job (ie. they are not just contrived/​chosen to get the result). So (Wonham et al claim) the interesting thing is that you can say that these isomorphisms hold in actual systems. Obviously there are a bunch of issues with this. I intentionally avoided too much discussion and criticism in this post and put it in a separate post.