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An efficient numerical algorithm for stability testing of fractional-delay systems.
Farshad Merrikh-Bayat1, Masoud Karimi-Ghartemani
1Sharif University of Technology, Tehran, Iran.
ISA Transactions
|November 14, 2008
Summary
This study introduces a novel numerical algorithm for testing the stability of fractional-delay systems. The method reliably identifies unstable poles, overcoming challenges with complex characteristic functions.
Area of Science:
- Control Systems Engineering
- Numerical Analysis
- Systems Theory
Background:
- Fractional-delay systems present unique challenges for stability analysis due to their multi-valued characteristic functions on Riemann surfaces.
- Traditional analytical methods struggle to locate roots of the characteristic equation in the right-half plane of the primary Riemann sheet.
- The origin as a branch point further complicates stability assessments for these systems.
Purpose of the Study:
- To develop a robust numerical algorithm for testing the Bounded-Input Bounded-Output (BIBO) stability of fractional-delay systems.
- To address the limitations of existing analytical techniques for stability analysis of these complex systems.
- To provide a method that not only determines stability but also identifies the location of unstable poles.
Main Methods:
- The proposed algorithm leverages Rouche's theorem to determine the number of zeros within a specified contour.
- It is specifically designed for systems with characteristic functions defined on Riemann surfaces with a finite number of sheets and a branch point at the origin.
- The numerical approach provides a practical solution for stability testing where analytical methods are insufficient.
Main Results:
- The algorithm reliably determines the BIBO stability of the considered class of fractional-delay systems.
- It accurately identifies both the number and the precise location of unstable poles.
- Validation through several illustrative examples confirms the algorithm's effectiveness and reliability.
Conclusions:
- The developed numerical algorithm offers a significant advancement for stability analysis of fractional-delay systems.
- It provides a practical and reliable tool for engineers and researchers working with these complex systems.
- The method's ability to locate unstable poles enhances its utility beyond simple stability determination.
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