Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 867932 19 pages doi 2011 867932 Research Article About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory M. De la Sen Faculty of Science and Technology University of the Basque Country 644 de Bilbao Leioa 48080 Bilbao Spain Correspondence should be addressed to M. De la Sen Received 9 November 2010 Accepted 31 January 2011 Academic Editor Marlene Frigon Copyright 2011 M. De la Sen. 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. 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. 1. Introduction Fractional calculus is concerned with the calculus of integrals and derivatives of any arbitrary real or complex orders. In this sense it may be considered as a generalization of classical calculus which is included in the theory as a particular case. There is a good compendium of related results with examples and case studies in 1 . Also there is an existing collection of results in the background literature concerning the exact and approximate
