Abstract
In this note, we develop a new characterization of stable polynomials. Specifically, given n positive, ordered numbers (frequencies), we develop a procedure for constructing a stable degree n monic polynomial with real coefficients. This construction can be viewed as a mapping from the space of n ordered frequencies to the space of stable degree n monic polynomials. The mapping is one-one and onto, thereby giving a complete parameterization of all stable, degree n monic polynomials. We show how the result can be used to generate parameterizations of stabilizing fixed-order proper controllers for unity feedback systems. We apply these results in the development of stability margin lower bounds for systems with parameter uncertainty.
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