Common diagonal solutions to the Lyapunov inequalities for interval systems

YILDIZ B., Büyükköroğlu T., Dzhafarov V.

Journal of Inequalities and Applications, vol.2016, no.1, 2016 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 2016 Issue: 1
  • Publication Date: 2016
  • Doi Number: 10.1186/s13660-016-1194-x
  • Journal Name: Journal of Inequalities and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: common diagonal solution, diagonal stability, interval matrices, Lyapunov inequality, minimax problem
  • Bilecik Şeyh Edebali University Affiliated: Yes

Abstract

© 2016, Yıldız et al.In this paper for interval systems we consider the problem of existence and evaluation of common diagonal solutions to the Lyapunov inequalities. For second order systems, we give necessary and sufficient conditions and exact solutions, that is, complete theoretical solutions. For third order systems, an algorithm for the evaluation of common solutions in the case of existence is given. In the general case a sufficient condition is obtained for a common diagonal solution in terms of the center and upper bound matrices of an interval family.