Common diagonal solutions to the Lyapunov inequalities for interval systems

Yildiz B., BÜYÜKKÖROĞLU T., Dzhafarov V.

JOURNAL OF INEQUALITIES AND APPLICATIONS, vol.2016, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2016
  • 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: interval matrices, Lyapunov inequality, diagonal stability, common diagonal solution, minimax problem, SUFFICIENT CONDITIONS, STABILITY, EXISTENCE, MATRICES
  • Anadolu University Affiliated: Yes

Abstract

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.