This paper deals with the problem of switching between several linear time-invariant (LTI) controllers-all of them capable of stabilizing a specific LTI process-in such a way that the stability of the closed-loop system is guaranteed for any switching sequence. We show that it is possible to find realizations for any given family of controller transfer matrices so that the closed-loop system remains stable, no matter how we switch among the controller. The motivation for this problem is the control of complex systems where conflicting requirements make a single LTI controller unsuitable.