Non-fragile control of switched systems with memory feedback based on convex optimization

Area of Science:

• Control Systems Engineering
• Systems Theory
• Nonlinear Control

Background:

• Discrete time-delay switched systems present unique control challenges.
• Robust stabilization aims to maintain system stability despite uncertainties and perturbations.
• Actuator saturation and controller perturbations (non-fragility) complicate control design.

Purpose of the Study:

• To design a non-fragile robust stabilization strategy for discrete time-delay switched systems.
• To develop a memory feedback control law and a switching law for enhanced stability.
• To ensure asymptotic stability at the origin with a maximized domain of attraction.

Main Methods:

• Utilized the switched Lyapunov functional approach for stability analysis.
• Derived sufficient conditions for non-fragile robust stabilization.
• Employed convex optimization with Linear Matrix Inequality (LMI) constraints to design the control law and maximize the region of attraction.

Main Results:

• Sufficient conditions for non-fragile robust stabilization were established.
• A non-fragile state feedback control law with memory was designed.
• The proposed method demonstrated effectiveness in numerical simulations, outperforming memoryless controllers in terms of state response and estimated domain of attraction.

Conclusions:

• The proposed switched Lyapunov functional approach effectively addresses non-fragile robust stabilization for discrete time-delay switched systems.
• Memory feedback control enhances system performance and robustness against perturbations and saturation.
• The LMI-based optimization provides a systematic way to design controllers that maximize the domain of attraction.