Delay-distribution-dependent stability and stabilization of T-S fuzzy systems with probabilistic interval delay

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Stochastic Systems

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling nonlinear systems.
• Time delays are common in real-world systems and can significantly impact stability.
• Analyzing T-S fuzzy systems with probabilistic interval delays presents unique challenges.

Purpose of the Study:

• To develop stability analysis and stabilization control design methods for T-S fuzzy systems with probabilistic interval delays.
• To derive delay-distribution-dependent criteria for mean-square exponential stability.
• To reduce conservatism in stability analysis for such systems.

Main Methods:

• Transformation of the original system into a T-S fuzzy model with stochastic parameter matrices.
• Utilizing the Lyapunov-Krasovskii functional method.
• Application of the parallel distributed compensation approach and matrix equation convexity.

Main Results:

• Derivation of delay-distribution-dependent criteria for mean-square exponential stability.
• Criteria consider both delay size and probability distribution within intervals.
• Demonstrated reduced conservatism compared to existing methods through practical examples.

Conclusions:

• The proposed method effectively addresses stability analysis and control design for T-S fuzzy systems with probabilistic interval delays.
• The developed criteria provide a less conservative approach by incorporating delay probability distribution information.
• The findings are applicable even when only the delay variation range is known.