A note on the stability of fractional order systems. (English) Zbl 1168.34036

Summary: 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.


34D20 Stability of solutions to ordinary differential equations
26A33 Fractional derivatives and integrals
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