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LMI-based stability analysis of fuzzy-model-based control systems using approximated polynomial membership functions.

Mohammand Narimani¹, H K Lam, R Dilmaghani

¹Division of Engineering, King's College London, London, UK. mohammad.narimani@kcl.ac.uk

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|November 25, 2010

Summary

New stability conditions for fuzzy-model-based control systems offer improved performance with imperfect premise matching. This research introduces relaxed linear-matrix-inequality conditions, reducing conservativeness in fuzzy control system analysis.

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Area of Science:

Control Systems Engineering
Fuzzy Logic Systems
Nonlinear Control Theory

Background:

Fuzzy model-based control systems (FMBCS) are widely used for complex nonlinear systems.
Stability analysis of FMBCS often faces challenges due to imperfect premise matching.
Existing stability conditions can be conservative, limiting practical application.

Purpose of the Study:

To propose novel, relaxed linear-matrix-inequality (LMI)-based stability conditions for FMBCS.
To address the issue of imperfect premise matching in fuzzy control systems.
To reduce the conservativeness associated with current stability analysis methods.

Main Methods:

Derivation of the Lyapunov function derivative, incorporating product terms of fuzzy model and controller membership functions.
Approximation of state variable relations using polynomials within partitioned operating domains.
Application of the S-procedure to mitigate conservativeness from global operating region considerations.

Main Results:

Development of new stability conditions that incorporate subsystem information and approximated polynomials.
Demonstration that previously established stability conditions are special cases of the proposed method.
Validation of the proposed approach through simulation examples.

Conclusions:

The proposed LMIs provide less conservative stability conditions for FMBCS with imperfect premise matching.
The method effectively handles the complexities arising from membership function partitioning and approximation.
The findings offer a more practical and robust framework for designing and analyzing fuzzy control systems.