Observer design for Takagi-Sugeno systems with unmeasurable premise variables using a non-quadratic Lyapunov function
Wail Hamdi1, Mohamed Yacine Hammoudi1, Madina Hamiane2
1Mohamed KHIDER University of Biskra, Algeria.
ISA Transactions
|August 29, 2024
Summary
This study reduces conservatism in nonlinear observers for Takagi-Sugeno fuzzy systems using non-quadratic Lyapunov functions. This approach offers computational efficiency and improved stability analysis for complex systems like induction motors.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear Systems Analysis
Background:
- Nonlinear observers for Takagi-Sugeno fuzzy systems often exhibit conservatism due to reliance on quadratic Lyapunov functions.
- Unmeasurable premise variables in fuzzy systems pose challenges for observer design and stability analysis.
Purpose of the Study:
- To reduce conservatism in nonlinear observers for Takagi-Sugeno fuzzy systems with unmeasurable premise variables.
- To develop a more effective stability analysis method using non-quadratic Lyapunov functions.
- To present an efficient computational approach for solving the derived Bilinear Matrix Inequalities.
Main Methods:
- Application of the Mean Value Theorem to address unmeasurable premise variables.
- Utilization of non-quadratic Lyapunov functions (NQLF) to decrease observer conservatism.
- Formulation of stability conditions as Bilinear Matrix Inequalities (BMI).
- Employing efficient linear solvers for BMI problem resolution.
Main Results:
- Demonstrated reduction in observer conservatism compared to previous quadratic Lyapunov function-based methods.
- Successfully formulated and solved stability conditions using Bilinear Matrix Inequalities.
- Validated the effectiveness and computational efficiency through a numerical example and real-time induction motor observer implementation.
Conclusions:
- The proposed method effectively reduces conservatism in nonlinear observers for Takagi-Sugeno fuzzy systems.
- The use of NQLF and efficient BMI solvers provides a practical and computationally feasible approach.
- The real-time implementation on an induction motor validates the observer's performance in complex, high-inequality scenarios.
Keywords:
Bilinear matrix inequalitiesMean value theoremPoly-quadratic Lyapunov functionTakagi–Sugeno fuzzy systemsMore Related Videos
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