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H(infinity) filtering for fuzzy singularly perturbed systems.

Guang-Hong Yang1, Jiuxiang Dong

  • 1Key Laboratory of Integrated Automation of Process Industry (Ministry of Education), and College of Information Scienceand Engineering, Northeastern University, Shenyang 110004, China. yangguanghong@ise.neu.edu.cn

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|September 12, 2008
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Summary
This summary is machine-generated.

This study presents a new method for designing H(infinity) filters for fuzzy singularly perturbed systems. The approach improves the bound of the singular-perturbation parameter (epsilon) using linear-matrix-inequality techniques.

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Area of Science:

  • Control Systems Engineering
  • Fuzzy Logic Systems
  • Nonlinear Systems Analysis

Background:

  • Singularly perturbed systems are common in control engineering, often exhibiting complex dynamics.
  • Designing effective H(infinity) filters is crucial for robust performance in these systems.
  • Existing methods may not optimally handle the singular-perturbation parameter (epsilon).

Purpose of the Study:

  • To develop a method for designing H(infinity) filters for fuzzy singularly perturbed systems.
  • To simultaneously design the H(infinity) filter and improve the bound of the singular-perturbation parameter (epsilon).
  • To evaluate the upper bound of epsilon for a prescribed H(infinity) performance.

Main Methods:

  • A linear-matrix-inequality (LMI)-based approach is proposed for simultaneous filter and parameter bound design.
  • The method is extended to cases where epsilon is not explicitly considered, reducing to existing LMI techniques.
  • A generalized eigenvalue problem is used to evaluate the upper bound of epsilon.

Main Results:

  • An LMI-based framework for designing H(infinity) filters and improving epsilon bounds in fuzzy singularly perturbed systems.
  • A method to determine the maximum allowable epsilon for a given H(infinity) performance level.
  • Numerical examples demonstrate the effectiveness of the proposed H(infinity) filter design and parameter bounding techniques.

Conclusions:

  • The proposed LMI-based approach effectively designs H(infinity) filters for fuzzy singularly perturbed systems.
  • The method allows for simultaneous optimization of filter performance and the singular-perturbation parameter bound.
  • The generalized eigenvalue problem provides a valuable tool for assessing system robustness concerning epsilon.