NDLI: Stability regions of fractional systems in the space of perturbed orders

Content Provider	IET Digital Library
Author	Rapaić, Milan R. Malti, Rachid
Abstract	When dealing with fractional order systems, perturbations in differentiation orders arise frequently due to issues with floating point arithmetics, or due to imprecisions of various order estimation algorithms. This study establishes new results regarding stability/instability of fractional systems with perturbed differentiation orders, knowing the related properties of their unperturbed counterparts. First of all, starting from a point in the space of differentiation orders, sufficient stability/instability conditions of all systems with differentiation orders varying along a line segment with a prescribed direction are established. Then, a continuation procedure is developed allowing computation of the maximum perturbation (along some given direction) which guarantees that the number of zeros in the closed right-half plane of the characteristic function remain unchanged. Finally, sufficient conditions are established guaranteeing stability/instability of all systems having differentiation orders within a domain. The established results allow concluding on the stability of incommensurate fractional transfer functions. They are illustrated by a number of examples, including an experimental one.
Starting Page	2610
Ending Page	2619
Page Count	10
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 16, Nov (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/16
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2018.6350
Journal	IET Control Theory & Applications
Publisher Date	2019-08-13
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Control System Analysis Differential Equation (numerical Analysis) Differentiation Floating Point Arithmetic Fractional Order System Fractional System Numerical Approximation And Analysis Order Estimation Algorithm Perturbed Differentiation Orders Perturbed Orders Stability Stability Region Synthesis Method Transfer Function
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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