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Robust stability of fractional order polynomials with complicated uncertainty structure
Radek Matušů1, Bilal Şenol2, Libor Pekař3
1Centre for Security, Information and Advanced Technologies (CEBIA-Tech), Faculty of Applied Informatics, Tomas Bata University in Zlín, Zlín, Czech Republic.
Plos One
|June 30, 2017
Summary
This study introduces a graphical method for robust stability analysis of fractional-order polynomials with complex uncertainties. The approach uses numerical calculations and value set depictions to ensure system stability.
Area of Science:
- Control Systems Engineering
- Applied Mathematics
- Numerical Analysis
Background:
- Robust stability analysis is crucial for systems with uncertainties.
- Fractional-order systems and quasi-polynomials present unique analytical challenges.
- Existing analytical tools are insufficient for complex uncertainty structures.
Purpose of the Study:
- To develop a graphical approach for robust stability analysis.
- To address complex uncertainty structures in fractional-order (quasi-)polynomials.
- To investigate multilinear, polynomial, general, and retarded quasi-polynomial uncertainties.
Main Methods:
- Numerical calculation of value sets.
- Graphical depiction of value sets.
- Application of the zero exclusion condition.
Main Results:
- A graphical method is presented for robust stability analysis.
- The method is applicable to families of fractional-order (quasi-)polynomials.
- Complex parametric and general uncertainty structures are handled.
Conclusions:
- The graphical approach provides a viable alternative to analytical methods.
- This method enhances the understanding of robust stability for complex systems.
- The zero exclusion condition is effectively applied using numerical value sets.
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