A nonlinear programming procedure and a necessary condition for the simultaneous stabilization of 3 or more linear systems

We frame the problem of finding a fixed controller to simultaneously stabilize, or co-stabilize, multiple systems as a nonlinear programming (NLP) problem. In the NLP problem, we can include the constraint that the controller be strong (stable) or bistable (stable and inverstable). We also present a necessary condition for the co-stabilization of 3 or more systems.