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Sampled-data fuzzy controller for time-delay nonlinear systems: fuzzy-model-based LMI approach.

H K Lam1, Frank H F Leung

  • 1Department of Electronic Engineering, Division of Engineering, The King's College London, London, UK.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|June 7, 2007
PubMed
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This study introduces a novel sampled-data fuzzy control system designed to improve stability and performance in nonlinear systems with time delays. The approach simplifies analysis and enhances control capabilities for digital implementation.

Area of Science:

  • Control Systems Engineering
  • Fuzzy Logic Systems
  • Nonlinear Control Theory

Background:

  • Sampled-data fuzzy control systems offer reduced implementation costs but introduce complexities due to sampling and time delays.
  • Traditional stability analysis for these systems is challenging compared to continuous-time counterparts.
  • Existing methods struggle with the inherent instability caused by sampling and time delays in nonlinear plants.

Purpose of the Study:

  • To propose a novel sampled-data fuzzy controller with enhanced nonlinearity compensation for systems with time delays.
  • To develop simplified stability and performance analysis methods using linear matrix inequality (LMI) techniques.
  • To reduce the complexity of stability analysis for sampled-data fuzzy control systems with time delays.

Main Methods:

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  • Utilized a fuzzy-model-based control approach for system design.
  • Derived linear matrix inequality (LMI)-based stability conditions for guaranteed system stability.
  • Employed a descriptor representation to simplify system dynamics and reduce the number of LMI conditions.

Main Results:

  • Successfully derived LMI-based conditions for stability analysis of the proposed sampled-data fuzzy control system.
  • Demonstrated reduced complexity in stability analysis through descriptor representation.
  • Incorporated membership function information to facilitate the satisfaction of stability conditions.

Conclusions:

  • The proposed sampled-data fuzzy controller enhances nonlinearity compensation and simplifies stability analysis.
  • The LMI-based approach effectively guarantees system stability and aids in performance design.
  • The method offers a practical and efficient solution for controlling nonlinear systems with time delays.