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Non-commensurate fractional linear systems: New results
Manuel D Ortigueira1, Gabriel Bengochea2
1CTS-UNINOVA and NOVA School of Science and Technology of NOVA University of Lisbon, Campus da FCT da UNL, Quinta da Torre, 2829-516 Caparica, Portugal.
Journal of Advanced Research
|September 14, 2020
Summary
This study introduces a parallel approach for non-commensurate fractional linear systems, utilizing recursive partial fraction decomposition and inversion for analysis. The findings offer new methods for handling complex fractional systems.
Area of Science:
- Control Systems Engineering
- Applied Mathematics
- Signal Processing
Background:
- Fractional linear systems are increasingly important in modeling complex phenomena.
- Existing methods often focus on commensurate fractional orders.
- Analyzing non-commensurate systems presents unique challenges.
Purpose of the Study:
- To develop a method for analyzing non-commensurate fractional linear systems.
- To adapt techniques from commensurate systems to the non-commensurate case.
- To provide a systematic approach for partial fraction decomposition and inversion.
Main Methods:
- A parallel computational approach is employed, mirroring techniques used for commensurate systems.
- A recursive procedure is utilized for partial fraction decomposition.
- Each resulting partial fraction is inverted using two distinct methods.
- Integer/fractional decomposition is also performed.
Main Results:
- The study successfully applies partial fraction decomposition to non-commensurate fractional linear systems.
- The recursive inversion method proves effective for the analyzed system types.
- Demonstration through examples validates the proposed decomposition and inversion techniques.
Conclusions:
- The presented parallel approach offers a viable method for analyzing non-commensurate fractional linear systems.
- The recursive decomposition and dual inversion techniques are effective.
- This work extends the applicability of fractional system analysis methods.
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