Stability analysis of special polynomials constructed from the classical orthogonal polynomials with provision for parametric uncertainty

Consideration was given to the Chebyshev, Hermite, Legendre, and Gegenbauer polynomials. Special polynomials of complex variable were generated from the orthogonal polynomials with the use of the proposed algorithm. For the nominal values of coefficients, stability of the generated polynomials was proved. Simple necessary conditions for robust stability of the general polynomials were derived and used to analyze the impact of the parametric uncertainty on stability of the special polynomials.