Generalized stability preserving maps

Matrix stability preserving maps can be used to provide a different characterization of the existence of a fixed order controller that robustly stabilizes a family of plants. In addition, stability preserving map tests can be used as the basis for robust controller synthesis/design methods. We develop additional stability preserving map tests and demonstrate their use for the robust stabilization of a physical system. Earlier work restricted the order of the controller to be one less than the order of the plant family. Here we allow controllers to have arbitrary order and show how this leads to the concept of a generalized stability preserving map. We conclude the paper with a discussion about tests for such maps