New sufficient conditions for strong simultaneous stabilization

In this brief paper we present sufficient conditions for the existence of a single stable controller to stabilize a set of n SISO plants: P1, P2, ..., Pn (strong simultaneous stabilization). As is well known this is equivalent to the existence of a single controller, not necessarily stable, to stabilize n+1 plants (simultaneous stabilization). The basic assumption required in the current paper is that all the plants have the same unstable zeros. A practical example of where such an assumption holds, is when each plant has the same pure delay which is approximated by a non-minimum phase rational function. The results here are applied to examples of this type.