Nonmonotonic observer-based fuzzy controller designs for discrete time T-S fuzzy systems via LMI

Area of Science:

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

Background:

• Discrete-time nonlinear systems pose control challenges.
• Takagi-Sugeno (T-S) fuzzy models are widely used for representing such systems.
• Existing Lyapunov function methods can be overly conservative.

Purpose of the Study:

• To develop a less conservative state feedback controller synthesis method.
• To design a Takagi-Sugeno (T-S) fuzzy observer.
• To combine observer and controller into an output feedback controller.

Main Methods:

• Utilizing nonmonotonic Lyapunov functions for controller design.
• Employing parallel distributed compensation (PDC) for state feedback.
• Designing a T-S fuzzy observer analogous to controller design.
• Solving linear matrix inequalities (LMIs) for controller and observer synthesis.

Main Results:

• A new, less conservative state feedback controller synthesis method is proposed.
• The T-S fuzzy observer design is presented.
• The separation theorem allows for combined output feedback control.
• The nonmonotonic Lyapunov method enables control in scenarios where other methods fail.

Conclusions:

• The proposed nonmonotonic Lyapunov-based method provides a less conservative approach to controller design for T-S fuzzy systems.
• The method allows for separate design and combination of observer and controller.
• Illustrative examples demonstrate superior performance compared to common quadratic, piecewise, or non-quadratic Lyapunov functions.