Robustness analysis of polynomials with polynomial parameter dependency using Bernstein expansion
1998
This paper considers the robust stability verification of polynomials with coefficients depending polynomially on parameters varying in given intervals. Two algorithms are presented, both rely on the expansion of a multivariate polynomial into Bernstein polynomials. The first one is an improvement of the so-called Bernstein algorithm and checks the Hurwitz determinant for positivity over the parameter set. The second one is based on the analysis of the value set of the family of polynomials and profits from the convex hull property of the Bernstein polynomials. Numerical results to real-world control problems are presented showing the efficiency of both algorithms.
Keywords:
- Orthogonal polynomials
- Bernstein polynomial
- Mathematical optimization
- Classical orthogonal polynomials
- Askey–Wilson polynomials
- Control theory
- Koornwinder polynomials
- Discrete orthogonal polynomials
- Power sum symmetric polynomial
- Difference polynomials
- Discrete mathematics
- Mathematics
- Gegenbauer polynomials
- Jacobi polynomials
- Hahn polynomials
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