The expanding system problem

The following problem is considered: suppose a controlled system S exists with the property that robust tracking and regulation occurs in each of the system´s local control agents, and that a new subsystem Snew, which has outputs to be regulated, is to be connected to S. It is desired to determine: when is it possible to find a local controller for Snew so that its outputs and all previous outputs are regulated, without the requirement of having to retune the previous controllers obtained in S? This is called the expanding system problem. It is shown that if Snew is controllable and observable, and if a solution exists to the robust servomechanism problem for Snew taken in isolation, then for all interconnections and for almost all interconnection gains, there exists a solution to this expanding system problem.