Further theoretical justification of the κ-samples variation approach for discrete-time takagi-sugeno fuzzy systems

Dong Hwan Lee, Jin Bae Park, Young Hoon Joo

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13 Citations (Scopus)

Abstract

Therecently developed k-samples variation approach is known as a powerful way to reduce the conservativeness of existing stability and stabilization conditions for discrete-time Takagi- Sugeno (T-S) fuzzy systems. In this approach, the Lyapunov functions under consideration are not necessarily decreasing at every sample but are allowed to decrease every k samples, which is evidently less restrictive than classical approaches. Consequently, less-conservative linear-matrix-inequality (LMI) conditions were derived. In addition, it was proved that, for two positive integers k1 and k2, if the condition for k = k1 is fulfilled, then those corresponding to k = k2 are also satisfied when k2 is the divisor of k1 . In this letter, we prove that, if the condition for k = k2 admits a solution, then those corresponding to anykκk2 are also solvable.

Original languageEnglish
Article number5674079
Pages (from-to)594-597
Number of pages4
JournalIEEE Transactions on Fuzzy Systems
Volume19
Issue number3
DOIs
Publication statusPublished - 2011 Jun 1

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All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computational Theory and Mathematics
  • Artificial Intelligence
  • Applied Mathematics

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