Robust Schur Stability of Polynomials with Polynomial Parameter Dependency

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Abstract

The paper considers the robust Schur stability verification of polynomials with coefficients depending polynomially on parameters varying in given intervals. A new algorithm is presented which relies on the expansion of a multivariate polynomial into Bernstein polynomials and is based on the decomposition of the family of polynomials into its symmetric and antisymmetric parts. It is shown how the inspection of both polynomial families on the upper half of the unit circle can be reduced to the analysis of two related polynomial families on the real interval [-1,1]. Then the Bernstein expansion can be applied in order to check whether both polynomial families have a zero in this interval in common.

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