Robust Stability of Multivariate Polynomials

  • Vladimir L. Kharitonov
Part of the Systems & Control: Foundations & Applications book series (SCFA)


This chapter deals with stability analysis of multivaric’ polynomials.The maximal class of polynomials is introduced such that polynomials of this class preserve stability under small variations of the coefficients. Basic properties of such stable polynomials are discussed. Some robust stability conditions are given.


Robust Stability Univariate Polynomial Multivariate Polynomial Stability Radius Stable Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Basu, On the multidimensional generalization of robustness of scattering Hurwitz property of complex polynomialsIEEE Trans. Circuits Syst.36:1159–1167, 1989.MATHCrossRefGoogle Scholar
  2. [2]
    S. Basu, On boundary implications of stability and positivity properties of multidimensional systemsProc. of IEEE78:614–626, 1990.CrossRefGoogle Scholar
  3. [3]
    N.K. Bose, Robust multivariable scattering Hurwitz interval polynomialLinear Algebra Appl.98:123–136, 1988.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    N.K. Bose, Edge property from end-points for scattering Hurwitz polynomialsAutomatica32:4, 655–657, 1996.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    A.C. Bartlett, C.V. Hollot, and L. Huang, Root locations of an entire polytope of polynomials: it suffices to check the edgesMath. Control Signals Syst. 1:61–71, 1988.MATHCrossRefGoogle Scholar
  6. [6]
    D. Hinrichsen and A.J. Pritchard, Real and complex stability radii: A survey; inControl of Uncertain SystemsBirkhäuser, Boston, 119–162, 1990.Google Scholar
  7. [7]
    V.L. Kharitonov and J.A. Torres Muñoz, Robust stability of multivariate polynomials part 1: Small coefficient perturbations, Multidimensional Syst.Signal Processing10:7–20, 1998.Google Scholar
  8. [8]
    V.L. Kharitonov, J.A. Torres Muñoz, and M.-I. Ramirez Sosa, Robust stability of multivariate polynomials Part 2: Polytopic coefficient variations, Multidimensional Syst.Signal Processing10:1–12, 1999.Google Scholar
  9. [9]
    J. Kogan, Computation of stability radius for families of bivariate polynomialsMultidimensional Syst. Signal Processing4:151–165, 1993.MATHCrossRefGoogle Scholar
  10. [10]
    B.T. Polyak and S.B. Shmulyian, Frequency domain criteria for robust stability of bivariate polynomials, IEEE Trans. Circuits and Sys. 1:Fundamental Theory Appl.41:161–167, 1994.Google Scholar
  11. [11]
    A. Rantzer, Stability conditions for polytopes of polynomialsIEEE Trans. Auto. Control37:79–89, 1992.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Vladimir L. Kharitonov

There are no affiliations available

Personalised recommendations