LMI-based stability conditions for interval type-2 fuzzy-model-based control systems

H. K. Lam, Mohammad Narimani, L. D. Seneviratne

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

27 Scopus citations

Abstract

This paper investigates the stability of the interval type-2 (IT2) fuzzy-model-based (FMB) control systems. An IT2 T-S fuzzy model is developed to represent the nonlinear plant subject to parameter uncertainties, which are captured by the lower and upper membership functions. An IT2 fuzzy model is then be proposed to close the feedback loop. It is not required that the IT2 fuzzy controller shares the same premise membership functions or the same number of fuzzy rules as those of the IT2 T-S fuzzy model. Consequently, it offers a greater design flexibility to the IT2 fuzzy controllers. However, the mismatched premise membership functions are not favourable to the development of stability conditions and thus leads to a conservative stability analysis result. In this paper, with the consideration of the lower and upper membership functions, which carry the information of the nonlinearities and parameter uncertainties of the nonlinear plant, the stability of the IT2 FMB control systems is investigated based on the Lyapunov stability theory. Stability conditions in terms of linear matrix inequalities are developed to guarantee the stability of the IT2 FMB control systems and synthesize the IT2 fuzzy controller. A simulation example is given to demonstrates the effectiveness of the proposed approach.

Original languageBritish English
Title of host publicationFUZZ 2011 - 2011 IEEE International Conference on Fuzzy Systems - Proceedings
Pages298-303
Number of pages6
DOIs
StatePublished - 2011
Event2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011 - Taipei, Taiwan, Province of China
Duration: 27 Jun 201130 Jun 2011

Publication series

NameIEEE International Conference on Fuzzy Systems
ISSN (Print)1098-7584

Conference

Conference2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011
Country/TerritoryTaiwan, Province of China
CityTaipei
Period27/06/1130/06/11

Keywords

  • Fuzzy Controller
  • Fuzzy-Model-Based Control
  • Interval Type-2
  • Linear Matrix Inequalities (LMIs)
  • Stability Analysis

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