Simultaneous fault detection and control design for switched systems with two quantized signals

Area of Science:

• Control Systems Engineering
• Signal Processing
• Systems Theory

Background:

• Switched systems are prevalent in various applications but are susceptible to faults.
• Quantization of signals in control systems introduces uncertainties that complicate fault detection and control design.
• Existing methods often struggle to robustly handle simultaneous fault detection and control under quantization.

Purpose of the Study:

• To develop a method for simultaneous fault detection and control design in switched systems with two quantized signals.
• To account for dynamic quantizer effects and associated errors.
• To ensure robust system performance in the presence of quantization.

Main Methods:

• Employing dynamic quantizers before the fault detector and control input.
• Formulating sufficient conditions for fault detector/controller existence using linear matrix inequalities (LMIs).
• Utilizing convex optimization to derive gains and quantizer range supremum.

Main Results:

• The proposed method achieves robust performance for switched systems with quantized signals.
• Sufficient conditions for the existence of the fault detector/controller are established.
• The method provides a systematic way to design fault detectors and controllers, optimizing quantizer parameters.

Conclusions:

• The developed approach effectively handles simultaneous fault detection and control for switched systems with dynamic quantization.
• The LMI framework and convex optimization offer a powerful tool for designing robust quantized control systems.
• The findings are validated through illustrative examples, demonstrating practical applicability.