ON THE ROBUST STABILITY OF POLYNOMIAL MATRIX FAMILIES


Buyukkoroglu T., Celebi G. , Dzhafaroy V.

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, vol.30, pp.905-915, 2015 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 30
  • Publication Date: 2015
  • Doi Number: 10.13001/1081-3810.3124
  • Title of Journal : ELECTRONIC JOURNAL OF LINEAR ALGEBRA
  • Page Numbers: pp.905-915
  • Keywords: Stability, Multivariate polynomial, Bernstein expansion, Companion matrix

Abstract

In this study, the problem of robust asymptotic stability of n x n, polynomial matrix family, in both continuous-time and discrete-time cases, is considered. It is shown that in the continuous case the problem can be reduced to positivity of two specially constructed multivariable polynomials, whereas in the discrete-time case it is required three polynomials. Number of examples are given, where the Bernstein expansion method and sufficient conditions from [L.H. Keel and S.P. Bhattacharya. Robust stability via sign-definite decomposition. IEEE Transactions on Automatic Control, 56(1):140-145, 2011.] are applied to test positivity of the obtained multivariable polynomials. Sufficient conditions for matrix polytopes and one interesting negative result for companion matrices are also considered.