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  • 标题:Upper Bounds for the Solution of the Parameter Dependent Lyapunov Equation
  • 本地全文:下载
  • 作者:S. Savov ; I. Popchev
  • 期刊名称:Cybernetics and Information Technologies
  • 印刷版ISSN:1311-9702
  • 电子版ISSN:1314-4081
  • 出版年度:2011
  • 卷号:11
  • 期号:3
  • 出版社:Bulgarian Academy of Science
  • 摘要:This research work considers the problem of scalar and matrix solution bounds derivation for one class of parameter dependent Lyapunov equations (PDLEs). It is assumed, that the coefficient matrix is a matrix polytope, where the uncertain vector is defined on the unit simplex. It is shown that this problem can be efficiently solved by making use of some previously obtained results, concerning the exact conditions for positive definiteness of homogeneous matrix polynomials (HMPs). The main contribution consists in the definition of two upper bounds − for the trace and the maximum eigenvalue of the solution of a PDLE. The applicability of these results is illustrated by a numerical example.
  • 关键词:Lyapunov equation; uncertain systems; matrix polytope; robust stability.
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