Local Stabilization for Discrete-Time Fuzzy System With Guaranteed Resilience via Structural Relaxation

Area of Science:

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

Background:

• Discrete-time Takagi-Sugeno fuzzy systems are widely used but can be computationally intensive.
• Conventional stabilization methods may exhibit conservatism and high computational burden.
• Existing resilient stabilization techniques often rely on user-defined hyperparameters, limiting practicality.

Purpose of the Study:

• To develop a novel approach for relaxed local stabilization of discrete-time Takagi-Sugeno fuzzy systems with guaranteed resilience.
• To reduce conservatism and computational complexity compared to existing methods.
• To enhance the practicality and numerical efficiency of resilient stabilization.

Main Methods:

• A novel Lyapunov function and nonparallel distributed compensation (non-PDC) control law are proposed within an augmented membership-quadratic framework.
• Structural relaxation is applied to intertemporal cross terms by relaxing symmetry constraints.
• A matrix-type threshold condition is introduced to overcome hyperparameter limitations.
• New structural relaxation lemmas based on orthogonal complements are developed.

Main Results:

• The proposed method achieves relaxed local stabilization with guaranteed resilience.
• Demonstrated reduction in conservatism and computational burden.
• Validation through benchmark examples shows improved performance and efficiency compared to existing approaches.
• The matrix-type threshold condition enhances practicality and numerical efficiency.

Conclusions:

• The developed method offers an effective and less conservative approach to resilient stabilization for discrete-time Takagi-Sugeno fuzzy systems.
• The novel framework and lemmas provide a computationally efficient and practical solution.
• The findings contribute to advancing the field of robust control for complex fuzzy systems.