H_∞ control for a class of singular systems with state time-varying delay

Area of Science:

• Control Theory
• Systems Engineering
• Nonlinear Dynamics

Background:

• Singular systems present unique control challenges due to their inherent properties.
• State time-varying delays introduce complexities in stability analysis and controller design.
• Achieving robust stability and performance (H_∞) is critical for practical applications.

Purpose of the Study:

• To design a dynamic feedback controller for singular systems with state time-varying delays.
• To ensure the closed-loop system is regular, impulse-free, and stable.
• To meet a specified H_∞ performance index.

Main Methods:

• Lyapunov-Krasovskii functional method for stability analysis.
• Development of delay-dependent sufficient criteria for controller existence.
• Explicit determination of dynamic feedback controller parameters.

Main Results:

• Sufficient criteria guaranteeing the existence of the dynamic feedback controller are derived.
• The criteria are delay-dependent, accounting for the time-varying nature of the delay.
• Numerical examples demonstrate the effectiveness of the proposed control approach.

Conclusions:

• The proposed dynamic feedback controller effectively stabilizes singular systems with state time-varying delays.
• The developed criteria provide a systematic way to design controllers with guaranteed H_∞ performance.
• The study offers a valuable contribution to the field of robust control for complex systems.