Delay-dependent anti-windup synthesis for stability of constrained state delay systems using pole-constraints

Area of Science:

• Control Systems Engineering
• Systems Theory
• Nonlinear Control

Background:

• Actuator saturation in control systems can lead to performance degradation and instability.
• State-delay systems present unique challenges in stability analysis and controller design.
• Anti-windup strategies are crucial for mitigating saturation effects in constrained control systems.

Purpose of the Study:

• To design an anti-windup compensator gain for state-delay systems with actuator input constraints.
• To ensure closed-loop asymptotic stability using constrained pole-positioning.
• To improve the time-domain performance of systems experiencing saturation.

Main Methods:

• Utilizing Delay-Dependent Lyapunov-Krasovskii functionals.
• Applying local sector conditions for stability analysis.
• Deriving a Linear Matrix Inequality (LMI) characterization for anti-windup gain design.
• Incorporating fixed state delay bounds and pole-position constraints into the LMI formulation.

Main Results:

• A novel LMI characterization for anti-windup gain design is presented.
• The derived method guarantees asymptotic stability for constrained state-delay systems.
• The proposed anti-windup strategy effectively nullifies slow dynamics at saturation.
• Comparative numerical examples demonstrate improved stability and time-domain performance.

Conclusions:

• The LMI-based anti-windup compensator design ensures stability for constrained state-delay systems.
• The method offers enhanced performance by addressing saturation-induced slow dynamics.
• This approach provides a robust framework for controlling systems with both state delays and actuator saturation.