An innovative bounded real lemma for singular fractional-order systems

Area of Science:

• Control Systems Engineering
• Mathematical Analysis

Background:

• Singular fractional-order systems (SFOS) present unique challenges in control design.
• The bounded real lemma is crucial for H∞ control but complex in its standard form for SFOS.

Purpose of the Study:

• To modify the bounded real lemma for SFOS, enabling the use of real variables instead of complex ones.
• To reduce conservatism in H∞ feedback controller design for SFOS.

Main Methods:

• Construction of an admissible set using a single real variable.
• Development of a generalized S-procedure.
• Conversion of H∞ norm inequalities into frequency domain inequalities (FDIs).
• Application of full-rank decomposition of the descriptor matrix.

Main Results:

• A single real-variable bounded real lemma for SFOS is derived.
• Complex variables in the bounded real lemma for SFOS are successfully replaced with real variables.
• Reduced conservatism in H∞ feedback controller design is demonstrated.

Conclusions:

• The proposed method effectively modifies the bounded real lemma for SFOS.
• The conversion from complex to real variables maintains the lemma's validity.
• Simulation examples validate the effectiveness and reduced conservatism of the approach.