Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: Partially known transition probabilities case

Min Kook Song, Jin Bae Park, Young Hoon Joo

Research output: Contribution to journalArticlepeer-review

34 Citations (Scopus)

Abstract

This paper focuses on the stability analysis and the stabilization problem for a discrete-time Markovian jump fuzzy systems (MJFSs) with time-varying delays and partially known transition probabilities. These systems are made more general, by relaxing the traditional assumption in MJFSs that all the transition probabilities must be completely known. The class of MJFSs considered is described by a fuzzy model composed of two levels: a crisp level that represents the jumps and a fuzzy level that represents the system nonlinearities. Based on a stochastic Lyapunov function, stability and stabilization conditions for the MJFSs with time-varying delays are derived in both the case of completely known transition probabilities and the case of partially known transition probabilities. The derived conditions are represented in terms of linear matrix inequalities (LMIs). Finally, a numerical example is used to illustrate the effectiveness of the proposed theorem.

Original languageEnglish
Pages (from-to)136-146
Number of pages11
JournalInternational Journal of Control, Automation and Systems
Volume11
Issue number1
DOIs
Publication statusPublished - 2013 Feb

Bibliographical note

Funding Information:
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No.:2012014088) and the Human Resources Development program(No. 20124030200040) of the Korea Institute of Energy Technology Evaluation and Planning (KETEP) grant funded by the Korea government Ministry of Knowledge Economy.

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications

Fingerprint

Dive into the research topics of 'Stability and stabilization for discrete-time Markovian jump fuzzy systems with time-varying delays: Partially known transition probabilities case'. Together they form a unique fingerprint.

Cite this