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

作者：Zhou, J.^*

来源：IET Control Theory and Applications, 2017, 11(16): 2753-2760.

DOI：10.1049/iet-cta.2016.1578

• stability criteria
• linear systems
• state-space methods
• complex-domain stability criteria
• fractional-order linear dynamical systems
• fractional commensurate order linear time-invariant state-space equations
• FCO-LTI state-space equations
• FCO transfer functions
• Cauchy integral contours
• stability conditions
• necessary conditions
• sufficient conditions
• Nyquist-like criteria
• locus plotting
• fractional calculus
• regular-order systems
• input-output dimensionality

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.

• 出版日期2017-11-3
• 单位河海大学