Robust Stability of Linear State Space Models Via Bernstein Polynomials

  • A. Vicino
  • M. Milanese
Part of the Progress in Systems and Control Theory book series (PSCT, volume 6)


This paper presents recent results on robust stability of state space systems affected by parameteric variations. The case in which system characteristic polynomial coefficients are polynomial or rational functions of uncertain physical parameters is considered. A method is proposed which uses Bernstein polynomial expansions to test stability of families of matrices generated by parameters belonging to a hyperrectangular unceratinty set. The algorithm allows one to check positivity of a multivariate polynomial over a box. In particular, it includes a very easy test to check if the polynomial reaches its extremal value at one of the vertices of the box. It is also shown that the algorithm deriving from this approach can be combined with an algorithm presented in previous papers to compute efficiently the structured stability margin. Some numerical examples are given showing that computational improvements over the existing algorithm may be obtained for several problems.


Robust Stability Stability Margin Bernstein Polynomial Multivariate Polynomial Combine Algorithm 
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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • A. Vicino
    • 1
  • M. Milanese
    • 2
  1. 1.Dipartimento di Sistemi e InformaticaUniversitá di FirenzeFirenzeItaly
  2. 2.Dipartimento di Automatica e InformaticaPolitecnico di TorinoTorinoItaly

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