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Dynamic output feedback H∞ control for 2D fuzzy systems.

Lizhen Li1, Xiaofeng Li2, Shuxia Ye3

  • 1The School of Mathematics and Physics, Shanghai University of Electric Power, Shanghai 200090, China.

ISA Transactions
|January 7, 2019
PubMed
Summary

This study introduces a new H-infinity control method for 2D discrete fuzzy systems. The approach guarantees noise attenuation without rank constraints, offering a robust solution for complex systems.

Keywords:
control2D fuzzy systemsBasis-dependent Lyapunov functionDynamic output feedback

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Area of Science:

  • Control Theory
  • Fuzzy Systems
  • Systems Engineering

Background:

  • Two-dimensional (2D) discrete fuzzy systems are crucial in modeling complex spatio-temporal phenomena.
  • The Fornasini-Marchesini state-space model is a standard framework for these systems.
  • Ensuring robust performance, specifically H-infinity noise attenuation, is a key challenge in control design.

Purpose of the Study:

  • To develop a dynamic output feedback H-infinity control strategy for 2D discrete fuzzy systems.
  • To establish sufficient criteria for guaranteeing H-infinity noise attenuation in the closed-loop system.
  • To present a controller design method applicable to both 2D and 1D discrete-time fuzzy systems without rank constraints on system matrices.

Main Methods:

  • Introduction of novel slacked matrices to formulate control conditions.
  • Derivation of sufficient criteria expressed as strict linear matrix inequalities (LMIs).
  • Application of the developed output feedback H-infinity controller design to 1D discrete-time fuzzy systems.

Main Results:

  • Sufficient criteria for H-infinity noise attenuation were successfully established.
  • The proposed controller design method demonstrated effectiveness and advantages through simulations.
  • The method avoids rank constraints on system matrices, enhancing its applicability.

Conclusions:

  • The developed dynamic output feedback H-infinity control approach provides a robust solution for 2D discrete fuzzy systems.
  • The LMI-based criteria offer a computationally tractable method for controller synthesis.
  • The approach is validated by simulation examples, confirming its practical utility and superiority.