Reducing conservatism in robust stability analysis of fractional-order-polytopic systems

Area of Science:

• Control Systems Engineering
• Systems Theory
• Applied Mathematics

Background:

• Fractional-order (FO) systems are increasingly important in modeling complex dynamics.
• Robust stability analysis for uncertain systems is crucial for reliable control.
• Existing methods like LMIs and exposed edges theorem are insufficient for FO LTI systems with polytopic uncertainty due to non-affine characteristic polynomials.

Purpose of the Study:

• To develop a novel method for robust stability analysis of fractional-order (FO) linear time-invariant (LTI) systems with polytopic uncertainty.
• To overcome limitations of existing robust stability analysis techniques for such systems.
• To provide a computationally feasible approach for assessing system stability.

Main Methods:

• An over-parameterization technique is employed to transform the system's characteristic polynomial.
• The main characteristic polynomial is converted into a set of local over-parameterized characteristic polynomials (LOPCPs).
• The robust stability of the uncertain system is evaluated by analyzing the robust stability of these LOPCPs using an algorithm based on the exposed edges idea.

Main Results:

• It is proven that the robust stability of the LOPCPs guarantees the robust stability of the original uncertain FO LTI system.
• A new algorithm is proposed for robust stability analysis, leveraging the properties of LOPCPs.
• Extensive examples demonstrate the superiority and feasibility of the proposed algorithm compared to existing methods.

Conclusions:

• The proposed over-parameterization technique effectively addresses the robust stability analysis of FO LTI systems with polytopic uncertainty.
• The developed algorithm provides a reliable and superior method for stability assessment in these complex systems.
• This work offers a valuable contribution to the field of fractional-order control systems and robust stability analysis.