Fault detection for T-S fuzzy time-delay systems: delta operator and input-output methods

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear System Analysis

Background:

• Takagi-Sugeno fuzzy systems are widely used for modeling complex nonlinear dynamics.
• Fault detection in these systems is crucial for safety and reliability, especially with time-varying delays.
• Existing methods often struggle with the complexities introduced by time-varying delays.

Purpose of the Study:

• To develop an effective fault detection strategy for Takagi-Sugeno fuzzy systems with time-varying delays.
• To convert the fault detection problem into a robust filtering problem using the delta operator approach.
• To ensure asymptotic stability and prescribed H-infinity disturbance attenuation for the fault detection system.

Main Methods:

• Approximation of time-varying delays using a two-term approximation method.
• Construction of a fuzzy augmented fault detection system in the delta-domain.
• Application of the scaled small gain theorem and a Lyapunov-Krasovskii functional for stability analysis.
• Derivation of a solvability condition for the fault detection filter.

Main Results:

• A sufficient condition for asymptotic stability with H-infinity disturbance attenuation is derived.
• A method for designing the fault detection filter is established.
• The filter design is reduced to solving a convex optimization problem, ensuring feasibility.

Conclusions:

• The proposed delta operator-based fault detection method is effective for Takagi-Sugeno fuzzy systems with time-varying delays.
• The method guarantees system stability and robust performance against disturbances.
• A numerical example validates the feasibility and effectiveness of the developed approach.