Computational geometry: an introduction
Computational geometry: an introduction
Convergent bounds for the range of multivariate polynomials
Proceedings of the International Symposium on interval mathematics on Interval mathematics 1985
Robust analysis and design of control systems using interval arithmetic
Automatica (Journal of IFAC)
Robust Control: Systems with Uncertain Physical Parameters
Robust Control: Systems with Uncertain Physical Parameters
The Bernstein polynomial basis: A centennial retrospective
Computer Aided Geometric Design
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The paper considersthe robust Schur stability verification of polynomials with coefficientsdepending polynomially on parameters varying in given intervals.A new algorithm is presented which relies on the expansion ofa multivariate polynomial into Bernstein polynomials and is basedon the decomposition of the family of polynomials into its symmetricand antisymmetric parts. It is shown how the inspection of bothpolynomial families on the upper half of the unit circle canbe reduced to the analysis of two related polynomial familieson the real interval [-1,1]. Then the Bernsteinexpansion can be applied in order to check whether both polynomialfamilies have a zero in this interval in common.