Iterative solutions of coupled discrete Markovian jump Lyapunov equations

Qing Wang, James Lam, Yimin Wei, Tongwen Chen

Research output: Contribution to journalArticlepeer-review

38 Citations (Scopus)

Abstract

In this paper, two iterative methods are given to solve coupled discrete Markovian jump Lyapunov equations arising from the stability analysis of discrete-time Markovian jump systems. When such equations have unique positive definite solutions, a sufficient condition for the convergence of iterates for one iterative method is derived. When such equations only have unique solutions, but not necessarily positive definite, the above iterative method may fail and an alterative iterative method is provided by using the solutions of discrete-time Lyapunov equations as its intermediate steps. A sufficient condition is also presented for the convergence of the iterates.

Original languageEnglish
Pages (from-to)843-850
Number of pages8
JournalComputers and Mathematics with Applications
Volume55
Issue number4
DOIs
Publication statusPublished - Feb 2008
Externally publishedYes

Keywords

  • Discrete-time systems
  • Lyapunov equations
  • Markovian systems

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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