An alternative LMI static output feedback control design for discrete-time nonlinear systems represented by...

Area of Science:

• Control Systems Engineering
• Nonlinear System Dynamics
• Mathematical Modeling

Background:

• Takagi-Sugeno (T-S) models are widely used for representing complex nonlinear systems.
• Designing static output feedback controllers for discrete-time nonlinear systems presents significant challenges.
• Existing methods often impose restrictive conditions, limiting their applicability.

Purpose of the Study:

• To develop a novel static output feedback controller design for discrete-time nonlinear systems.
• To achieve less demanding design conditions compared to current approaches.
• To enhance the flexibility and applicability of controller synthesis for T-S models.

Main Methods:

• Utilizing Takagi-Sugeno models for exact system representation.
• Incorporating past states into both the control law and Lyapunov function.
• Formulating controller design conditions using linear matrix inequalities (LMIs).

Main Results:

• The proposed method yields more relaxed conditions for controller design.
• The inclusion of past states in the control law and Lyapunov function is key to improved results.
• Numerical examples demonstrate the effectiveness and less demanding nature of the proposed conditions.

Conclusions:

• The presented static output feedback controller design offers a significant improvement for discrete-time nonlinear Takagi-Sugeno systems.
• The approach provides a more flexible and less conservative alternative to existing methods.
• This work contributes to advancing the theory and practice of robust control for nonlinear systems.