Lower triangle factor based sliding mode observers design for T-S fuzzy systems with faults

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Fault Diagnosis

Background:

• Takagi-Sugeno (T-S) fuzzy systems are widely used for modeling complex nonlinear systems.
• Accurate fault estimation is crucial for maintaining the performance and safety of these systems.
• Existing fault estimation methods often lack a unified framework.

Purpose of the Study:

• To propose a novel synthetic estimation observer design for T-S fuzzy systems with faults.
• To develop a unified framework encompassing robust, adaptive, and intermediate estimation observers.
• To design a Linear Transformation Function (LTF)-based sliding mode observer (SMO) for enhanced fault estimation.

Main Methods:

• A synthetic estimation observer design methodology is introduced.
• An LTF-based sliding mode observer (SMO) is specifically designed for T-S fuzzy systems.
• Linear Matrix Inequality (LMI)-based conditions are derived to ensure stability and boundedness of error dynamics.

Main Results:

• The proposed synthetic observer unifies existing observer types.
• The LTF-based SMO effectively estimates faults in T-S fuzzy systems.
• LMI-based conditions guarantee uniform ultimate boundedness of the error states.

Conclusions:

• The developed synthetic estimation observer provides a generalized approach for fault estimation in T-S fuzzy systems.
• The LTF-based SMO demonstrates effective fault estimation capabilities.
• The LMI-based conditions ensure the stability and reliability of the fault estimation process.