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An Optimal Divisioning Technique to Stabilization Synthesis of T-S Fuzzy Delayed Systems
IEEE Transactions on Cybernetics
|April 15, 2016
Summary
This study presents a new stability condition for Takagi-Sugeno (T-S) fuzzy systems with time-varying delays. The proposed method enhances stability analysis and controller design for fuzzy delayed systems.
Area of Science:
- Control Systems Engineering
- Fuzzy Logic Systems
- Nonlinear System Analysis
Background:
- Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling complex nonlinear systems.
- Time-varying delays introduce significant challenges in stability analysis and controller design.
- Existing methods for delayed T-S fuzzy systems often suffer from conservatism.
Purpose of the Study:
- To develop a less conservative stability condition for T-S fuzzy systems with time-varying delays.
- To design a state-feedback fuzzy controller for these systems.
- To provide a systematic method for controller parameter derivation.
Main Methods:
- Lyapunov-Krasovskii functional construction.
- Reciprocally convex lemma application.
- Delay partitioning approach for reduced conservatism.
- Parallel distributed compensation (PDC) for controller design.
- Linear Matrix Inequality (LMI) optimization.
Main Results:
- A novel sufficient stability condition for T-S fuzzy systems with time-varying delays is proposed.
- The new condition significantly reduces conservatism compared to existing results.
- A state-feedback fuzzy controller is designed based on the stability condition.
- Controller parameters are efficiently derived using LMI optimization.
Conclusions:
- The proposed technique effectively addresses stability analysis and stabilization for T-S fuzzy systems with time-varying delays.
- The delay partitioning approach combined with Lyapunov-Krasovskii functionals offers improved performance.
- The method is validated through simulations, including the inverted pendulum benchmark.
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