Line Integral Approach to Extended Dissipative Filtering for Interval Type-2 Fuzzy Systems

Area of Science:

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

Background:

• Interval type-2 (IT2) fuzzy systems present unique challenges in stability analysis and filter design.
• Extended dissipativity is a crucial concept for analyzing the performance and robustness of dynamic systems.
• Existing methods often rely on quadratic Lyapunov functions, which may not be sufficient for complex IT2 fuzzy systems.

Purpose of the Study:

• To develop a novel approach for extended dissipativity analysis of IT2 fuzzy systems.
• To design an extended dissipative filter that guarantees asymptotic stability for the filtering error system.
• To establish a more general condition for stability and extended dissipativity compared to existing methods.

Main Methods:

• Utilizing a line integral Lyapunov function to derive a sufficient condition for asymptotic stability and extended dissipativity.
• Employing congruence transformation and change of variables to establish a linear matrix inequality (LMI)-based equivalent condition.
• Developing an extended dissipative filter through a parameterization method.

Main Results:

• A novel sufficient condition for asymptotic stability and extended dissipativity is established for IT2 fuzzy systems.
• An LMI-based condition, more general than those using common quadratic Lyapunov functions, is derived.
• A new extended dissipative filter is designed, guaranteeing stability and extended dissipativity for the filtering error system.
• The proposed filter encompasses existing methods as a special case.

Conclusions:

• The developed line integral Lyapunov function approach provides a more general framework for extended dissipativity analysis in IT2 fuzzy systems.
• The proposed LMI-based condition and filter design enhance the robustness and performance guarantees for these systems.
• Simulation examples validate the effectiveness and advantages of the proposed methodology over existing techniques.