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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
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.
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.
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