Controller design for TS models using delayed nonquadratic Lyapunov functions.

Area of Science:

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

Background:

• Nonquadratic Lyapunov functions are increasingly vital for Takagi-Sugeno fuzzy model analysis and controller design.
• Existing methods often have limitations in terms of conservatism and scope.

Purpose of the Study:

• To develop relaxed conditions for controller design using nonquadratic Lyapunov functions and delayed controllers.
• To establish a general framework for employing nonquadratic Lyapunov functions in control design.
• To enhance existing state-of-the-art methods for Takagi-Sugeno fuzzy systems.

Main Methods:

• Utilizing nonquadratic Lyapunov functions for stability analysis.
• Incorporating delayed controllers into the design framework.
• Developing two novel controller design methodologies within a generalized framework.

Main Results:

• The proposed controller design methods provide less conservative conditions.
• The new methods demonstrate superior performance over current state-of-the-art techniques.
• The framework successfully generalizes existing approaches.

Conclusions:

• The developed framework offers a more flexible and powerful approach to controller design for Takagi-Sugeno fuzzy models.
• The proposed methods are effective for robust control, H∞ control, and α-sample variation problems.
• This work advances the application of nonquadratic Lyapunov functions in modern control theory.