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About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory

Fixed Point Theory and Applications20112011:867932

Received: 9 November 2010

Accepted: 31 January 2011

Published: 24 February 2011


This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The investigation is performed via fixed point theory in a complete metric space by defining appropriate nonexpansive or contractive self-mappings from initial conditions to points of the state-trajectory solution. The existence of a unique fixed point leading to a globally asymptotically stable equilibrium point is investigated, in particular, under easily testable sufficiency-type stability conditions. The study is performed for both the uncontrolled case and the controlled case under a wide class of state feedback laws.


Equilibrium PointAsymptotic StabilityFractional OrderState FeedbackPoint Theory

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Authors’ Affiliations

Faculty of Science and Technology, University of the Basque Country, Bilbao, Spain


© M. De la Sen. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.