A note on the stability of fractional order systems

Authors:
Mohammad Saleh Tavazoei;Mohammad Haeri
Affiliations:
Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran;Advanced Control System Laboratory, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran
Venue:
Mathematics and Computers in Simulation
Year:
2009

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Abstract

In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems.