Extended dissipative filter design for T-S fuzzy systems with multiple time delays

Area of Science:

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

Background:

• Nonlinear time-delay systems pose challenges in control and filtering.
• Existing fuzzy filtering methods often address performance constraints separately.
• Communication delays in filters are increasingly relevant but less studied.

Purpose of the Study:

• To develop a unified framework for fuzzy filtering of nonlinear time-delay systems.
• To incorporate H∞, L2-L∞, and dissipative performance constraints simultaneously.
• To design filters that account for communication delays.

Main Methods:

• Application of the extended dissipativity concept for unified performance analysis.
• Design of fuzzy filters with communication delays.
• Utilization of a novel fuzzy Lyapunov-Krasovskii functional.
• Derivation of delay-dependent conditions for stability and performance.
• Formulation of Linear Matrix Inequality (LMI)-based conditions for filter existence.

Main Results:

• A unified approach is presented for H∞, L2-L∞, and dissipative fuzzy filtering.
• Delay-dependent conditions for the filtering error system's stability and performance are derived.
• LMI-based conditions enable the calculation of filter parameters.
• The proposed method is validated through an illustrative example.

Conclusions:

• The proposed method effectively addresses fuzzy filtering for nonlinear time-delay systems with multiple performance criteria.
• The inclusion of communication delays makes the filter design more general and practical.
• The LMI-based approach provides a systematic way to synthesize the required filters.