Finite frequency tests for robust stability

Being able to discern the robust stability of a polynomial with coefficients that depend on parameters, is of fundamental importance in control systems analysis. Not only does this allow one to verify the robust stability of some feedback loop, but also confirm other important performance characteristics. Consequently, the development of efficient robust stability tests is of high priority. In this paper, we focus attention on the problem of robust stability of polynomial families with real parameter uncertainty. Several families are considered, with coefficients that depend on parameters in a polynomic fashion. We show that for these families, one can provide efficient finite frequency tests for robust stability.