Controller synthesis and the simultaneous stabilization of polynomials

The authors first demonstrate that finding a controller that simultaneously stabilizes the required polynomials is equivalent to finding a controller that simultaneously stabilizes a finite number of plants. These plants include the true vertex plants as well as a number of fictitious vertex plants which involve the controller, however. The authors then manipulate the feedback interconnections and express them in terms of the additive, multiplicative, and divisive models. Once this is done, the system is an appropriate framework in which other solution methods can be applied (H_∞, for example). This makes it possible to address questions of controller existence and synthesis and make comparisons of conservatism. It is demonstrated with an example how an H_∞ robust controller design can be enhanced by employing the 4^k-polynomial concept