ON THE ROBUST STABILITY OF POLYNOMIAL MATRIX FAMILIES

Buyukkoroglu T., Celebi G., Dzhafaroy V.

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, cilt.30, ss.905-915, 2015 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 30
  • Basım Tarihi: 2015
  • Doi Numarası: 10.13001/1081-3810.3124
  • Dergi Adı: ELECTRONIC JOURNAL OF LINEAR ALGEBRA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.905-915
  • Anahtar Kelimeler: Stability, Multivariate polynomial, Bernstein expansion, Companion matrix
  • Yozgat Bozok Üniversitesi Adresli: Hayır

Özet

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.