What is it about?

A new results have been established regarding stability/instability of fractional systems with perturbed differentiation orders. We assume that stability (or instability) has been established for a specific fractional or integer order system, and investigate how much differentiation orders can be perturbed without changing the number of unstable poles in the right half of the complex plane.

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Why is it important?

It is often not trivial to investigate stability of fractional order systems, especially if those systems are of non-commensurate order. The procedure in the present paper enables one to investigate stability of such systems indirectly, by first establishing stability of a related commensurate order, or even integer order system. In addition, small perturbations in differentiation orders often arise due to implementation issues related to floating-point arithmetic. The present paper gives a possibility to ascertain stability in the presence of such perturbations.


The proposed algorithm is based on frequency-domain analysis, and is therefore - in principle - no limited to perturbations in the differentiation orders only, nor to the fractional order systems in particular. Extension to other classes of linear systems seems promising.

Milan Rapaić
University of Novi Sad, Faculty of Technical Sciences

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This page is a summary of: On stability regions of fractional systems in the space of perturbed orders, IET Control Theory and Applications, August 2019, the Institution of Engineering and Technology (the IET), DOI: 10.1049/iet-cta.2018.6350.
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