Stability preserving maps and robust stabilization

The notion of a stability preserving map can be defined in a number of ways. In this paper we introduce one such definition and then demonstrate its impact on the problem of robust controller synthesis. Specifically, we show that the concept of a stability preserving map can be used to provide a different characterization of the existence of a fixed order controller that simultaneously stabilizes a finite number of plants. We also demonstrate how it can be used to state conditions for the robust stabilization of families of plants with real parameter uncertainty. In addition, the characterization provides new insight into how to construct robustly stabilizing controllers.