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A Sufficient Condition for Checking the Attractiveness of a Sliding Manifold in Fractional Order Sliding Mode Control
Author(s) -
Efe Mehmet Önder
Publication year - 2012
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.430
Subject(s) - attractiveness , order (exchange) , stability (learning theory) , mode (computer interface) , mathematics , manifold (fluid mechanics) , integer (computer science) , control theory (sociology) , control (management) , fractional calculus , law , computer science , engineering , economics , political science , finance , artificial intelligence , philosophy , mechanical engineering , programming language , machine learning , operating system , aesthetics
Abstract Stability issues of fractional order sliding mode control laws are analyzed in this paper. For differentiation orders less than unity, it is shown that a stable reaching law in the fractional order case corresponds to a stable reaching law in the integer order case. The contribution of the current study is to explain the stability of the closed loop by the use of the Caputo and Riemann‐Liouville definitions of fractional order differentiation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society