Piecewise H infinity: controller design of discrete time fuzzy systems

Area of Science:

• Control Systems Engineering
• Fuzzy Logic Systems
• Nonlinear Control Theory

Background:

• Discrete time fuzzy systems require robust control strategies for stability and performance.
• Existing H infinity control methods may not fully address the complexities of fuzzy system dynamics.
• Piecewise Lyapunov functions offer a flexible approach for stability analysis in complex systems.

Purpose of the Study:

• To develop a new H infinity controller design methodology specifically for discrete time fuzzy systems.
• To ensure global stability and H infinity-disturbance attenuation performance for the closed-loop fuzzy control systems.
• To provide a computationally tractable approach for controller synthesis.

Main Methods:

• Design of an H infinity controller based on discrete time fuzzy system models.
• Utilization of piecewise Lyapunov functions to establish global stability guarantees.
• Formulation of the control law design as a set of solvable linear matrix inequalities (LMIs).

Main Results:

• A novel H infinity controller design method for discrete time fuzzy systems is presented.
• The proposed method guarantees global stability and H infinity-disturbance attenuation.
• Control laws are derived by solving numerically tractable LMIs.

Conclusions:

• The developed H infinity controller design method effectively addresses discrete time fuzzy systems.
• The use of piecewise Lyapunov functions ensures robust stability and performance.
• The LMI-based approach offers a practical and efficient solution for controller implementation.