Non-fragile H∞ output feedback control design for continuous-time fuzzy systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Control Theory

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling complex nonlinear systems.
• Designing robust controllers for T-S systems with uncertainties and disturbances is challenging.
• Controller and observer gain variations (fragility) can degrade system performance.

Purpose of the Study:

• To develop a non-fragile H∞ fuzzy control design for continuous T-S fuzzy systems.
• To address uncertainties, external disturbances, and unmeasurable states.
• To ensure asymptotic stability and H∞ performance in the presence of gain variations.

Main Methods:

• Utilizing a fuzzy Lyapunov function approach.
• Introducing slack variables for improved conditions.
• Formulating sufficient stabilization conditions as Linear Matrix Inequalities (LMIs).
• Employing convex optimization for solving the LMIs.

Main Results:

• A new non-fragile control design scheme is proposed.
• Sufficient conditions for asymptotic stability and H∞ performance are derived.
• The proposed method effectively handles controller and observer gain variations.
• Numerical examples demonstrate the effectiveness of the proposed approach.

Conclusions:

• The developed non-fragile H∞ fuzzy control design provides a robust solution for T-S fuzzy systems.
• The LMI-based conditions offer a computationally tractable method for controller synthesis.
• The approach successfully guarantees system stability and H∞ performance under uncertainties and gain variations.