Complex-domain stability criteria for fractional-order linear dynamical systems

J. Zhou

Complex-domain stability criteria for fractional-order linear dynamical systems

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Author(s): J. Zhou¹
- Affiliations: 1: Department of Automatic Control Engineering, College of Energy and Electrical Engineering , Hohai University , Nanjing 211100 , People's Republic of China
Source: Volume 11, Issue 16, 03 November 2017, p. 2753 – 2760
DOI: 10.1049/iet-cta.2016.1578 , Print ISSN 1751-8644, Online ISSN 1751-8652

Received 17/12/2016, Accepted 03/08/2017, Revised 05/06/2017, Published 07/08/2017

This paper proposes stability criteria claimed in complex domains for dynamical systems that are described by fractional commensurate order linear time-invariant (FCO-LTI) state-space equations (thus endowed with FCO transfer functions) by means of the argument principle in complex analysis. Based on appropriate Cauchy integral contours or their shifting ones, the stability conditions are necessary and sufficient, without inter-domain transformation and independent of pole/eigenvalue computing and distribution testing. The proposed criteria are implementable graphically with locus plotting as using Nyquist-like criteria or numerically without locus plotting. The criteria apply to a variety of FCO-LTI systems, which can be single and multiple in fractional calculus, scalar and multivariable in input/output dimensionality. The criteria can also be exploited in regular-order systems without modification. Case studies are included to illustrate the main results.

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Complex-domain stability criteria for fractional-order linear dynamical systems

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