Stabilization of fractional-order singular uncertain systems

Area of Science:

• Control Systems Engineering
• Nonlinear Dynamics
• Mathematical Systems Theory

Background:

• Fractional-order systems (FOS) introduce complexities in stability analysis due to their non-integer order dynamics.
• Singular systems present challenges in control design due to inherent algebraic constraints.
• Robust control is crucial for systems operating under uncertainty.

Purpose of the Study:

• To develop state and static output feedback stabilization methods for fractional-order singular (FOS) uncertain linear systems.
• To guarantee the robust asymptotical stability of the closed-loop control systems.
• To provide effective controller synthesis techniques for FOS systems.

Main Methods:

• Utilizing matrix singular value decomposition (SVD) for system analysis.
• Applying linear matrix inequality (LMI) techniques for controller design.
• Deriving sufficient conditions for robust asymptotical stability.

Main Results:

• Sufficient conditions for robust asymptotical stability of FOS systems are established.
• New LMI-based results are developed for state and static output feedback controller synthesis.
• The effectiveness of the proposed methods is demonstrated through three numerical examples.

Conclusions:

• The proposed LMI-based approach provides a systematic way to design stabilizing controllers for FOS uncertain linear systems.
• The methods ensure robust asymptotical stability, crucial for practical applications.
• The numerical examples validate the efficacy of the developed feedback control strategies.