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On the stability and control of continuous-time TSK fuzzy systems.
Saeed Jafarzadeh1, M Sami Fadali
1Department of Computer and Electrical Engineering and Computer Science, California State University Bakersfield, Bakersfield, CA 93311, USA. sjafarzadeh20@gmail.com
IEEE Transactions on Cybernetics
|June 13, 2013
Summary
This study presents novel stability tests and control designs for continuous-time Takagi-Sugeno-Kang systems, even those with unstable or unstabilizable components, outperforming existing methods.
Area of Science:
- Control Theory
- Fuzzy Systems Engineering
Background:
- Traditional Lyapunov function methods struggle with systems featuring unstable consequents.
- Existing control designs often fail for systems with unstabilizable consequents.
Purpose of the Study:
- Introduce a new stability test for continuous-time (CT) Takagi-Sugeno-Kang (TSK) systems.
- Develop a control design methodology applicable to type-1 and type-2 CT TSK systems, including those with unstable or unstabilizable consequents.
Main Methods:
- Stability analysis using the comparison principle with a discontinuous function and upper right-hand derivative.
- Control design via fuzzy proportional and fuzzy proportional-integral controllers solved using linear matrix inequalities.
Main Results:
- Novel stability criteria applicable to systems with unstable consequents.
- Effective controller designs for systems with unstabilizable consequents.
- Demonstrated superiority over existing methods through illustrative examples.
Conclusions:
- The proposed methodology offers robust stability testing and controller design for a broader class of CT TSK systems.
- This approach overcomes limitations of common Lyapunov function-based methods and provides solutions where others fail.
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