Robust control design using stable polynomial parameterizations

A new parameterization of stable polynomials has recently been shown to facilitate robust control analysis and design. In this parameterization a stable degree n polynomial is uniquely identified with a set of ordered frequencies. Here we continue to explore properties of this parameterization and develop a relationship between these frequencies and the "bandwidth" associated with the polynomial. We then consider a feedback robust stability margin problem and show how the parameterization can be used to generate analytic expressions for stability margin lower bounds. In many cases these bounds are reasonably tight and can be exploited in robust analysis and design. We continue the development of ordinal optimization methods for robust control design and demonstrate how searches for higher order controllers can be improved by using information "discovered" from common properties of good lower order controllers. We also show how the parameterization can be used to enhance finite inclusions theorem based robust design.