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Functional approach to observability and controllability of linear fractional dynamical systems
*Venkatesan GovindarajCorresponding authorgovindaraj.maths@gmail.comDepartment of Mathematics, Indian Institute of Space Science and TechnologyThiruvananthapuram, 695547, IndiaView full profile →
, Raju K GeorgeDepartment of Mathematics, Indian Institute of Space Science and TechnologyThiruvananthapuram, 695547, IndiaView full profile →
* Corresponding author · click or hover a name for details
In this paper, a set of equivalent conditions for observability and controllability of linear fractional dynamical systems represented by the fractional differential equation in the sense of Caputo fractional derivative of order α ϵ (0,1] are established by using the tools of linear bounded operators. Examples are included to illustrate the theoretical results.
K.Balachandran, J.Kokila, On the controllability of fractional dynamical system , International Journal of Applied Mathematics and Computer Science, 22 ( 3 ), 523 – 531 ( 2012 ). K.Balachandran, V.Govindaraj, M.D.Ortigueira, M.Rivero, J.J.Trujillo, Observability and controllability of fractional linear dynamical systems, 6th Workshop on Fractional Differentiation and Its Applications, Grenoble, France, February 4–6, (2013) . K.Balachandran, J.Y.Park, J.J.Trujillo, Controllability of nonlinear fractional dynamical systems , Nonlinear Analysis, 75 ( 4 ), 1919 – 1926 ( 2012 ). K.Balachandran, V.Govindaraj, M.Rivero, J.A.Tenreiro Machado, J.J.Trujillo, Obervability of linear and nonlinear fractional order dynamical systems, Abstract and Applied Analysis, Article ID 346041 (2013) . K.Balachandran, V.Govindaraj, L.Rodryguez-Germa, J.J.Trujillo, Stabilizability of fractional dynamical systems , Fractional Calculus & Applied Analysis, 17 ( 2 ), 511 – 531 ( 2014 ). A.Bensoussan, G.D.Prato, M.C.Delfour, S.K.Mitter, Representation and Control of Infinite Dimensional Systems , Springer , New York ( 2006 ). J.Bisquert, Interpretation of a fractional diffusion equation with nonconserved probability density in terms of experimental systems with trapping or recombination , Physical Reviews E, 14 , 011109 – 011114 ( 2005 ). M.Bettayeb, S.Djennoune, New results on the controllability and observability of fractional dynamical systems , Journal of Vibration and Control, 14 ( 9–10 ), 1531 – 1541 ( 2008 ). Y.Chen, H.S.Ahn, D.Xue, Robust controllability of interval fractional order linear time invariant systems , Signal Processing, 86 ( 10 ), 2794 – 2802 ( 2006 ). M.Caputo, Linear model of dissipation whose Q is almost frequency independent-II , Geoph. J. Royal Astr. Soc., 13 ( 5 ), 529 – 539 ( 1967 ). L.Debnath, P.Mikusinski, Introduction to Hilbert Spaces with Applications, Academic Press , Burlington ( 2005 ). D.Diethelm, The Analysis of Fractional Differential Equations, Springer , Heidelberg ( 2010 ). S.Guermah, S.Djennoune, M.Bettayeb, Controllability and observability of linear discretetime fractional-order systems , International Journal of Applied Mathematics and Computer, 18 ( 2 ), 213 – 222 ( 2008 ). T.L.Guo, Controllability and observability of impulsive fractional linear time-invariant system , Computers and Mathematics with Applications, 64 ( 10 ), 3171 – 3182 ( 2012 ). A.A.Kilbas, M.Rivero, J.J.Trujillo, Existence and uniqueness theorems for differential equations of fractional order in weighted spaces of continuous functions , Fractional Calculus and Applied Analysis, 6 ( 4 ), 363 – 400 ( 2003 ). A.A.Kilbas, H.M.Srivastava, J.J.Trujillo, Theory and Applications of Fractional Differential Equation, Elsevier , Amsterdam ( 2006 ). F.Mainardi, Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models, Imperial College Press , London ( 2010 ). F.Mainardi, Fractional calculus: some basic problems in continuum and statistical mechanics , in: Fractals and Fractional Calculus in Continuum Mechanics (Eds. A.Carpinteri and F.Mainardi), Springer Verlag , Wien, 291 – 348 ( 1997 ). F.Mainardi, R.Gorenflo, On Mittag-Leffler type functions in fractional evolution processes , Journal of Computational and Applied Mathematics, 118 ( 1–2 ), 283 – 299 ( 2000 ). D.Matignon and B.d’Andrea-Novel, Some results on controllability and observability of finite dimensional fractional differential systems, Proceedings of the IAMCS, IEEE Conference on Systems, Man and Cybernetics Lille, France, July 9–12, 952–956 (1996) . D.Matignon, Optimal control of fractional systems: a diffusive formulation. In: 19th International Symposiu on Mathematical Theory of Networks and Systems. Hungary (2010) . D.Mozyrska, D.F.M.Torres, Minimal modified energy control for fractional linear control systems with the Caputo derivative , Carpathian Journal of Mathematics, 26 ( 2 ), 210 – 221 ( 2010 ). D.Mozyrska, D.F.M.Torres, Modified optimal energy and initial memory of fractional continuous-time linear systems , Signal Processing, 91 ( 3 ), 379 – 385 ( 2011 ). I.Podlubny, Fractional Differential Equations, Academic Press , ( 1999 ). A.E.Taylor, D.C.Lay, Introduction to Functional Analysis, John Wiley & sons , Canada, ( 1980 ). D.Valerio, J.J. Trujillo, M.Rivero, J. A.Tenreiro Machado, D.Baleanu, Fractional Calculus: A survey of useful formulas . The European Physical Journal Special Topics222 ( 8 ), 1825 – 1844 ( 2013 ). B.M.Vinagre, C.A.Monje, A.J.Calderon, Fractional order systems and fractional order control actions, in: Lecture 3 of the IEEE CDCO2 TW# 2: Fractional Calculus Applications in Automatic Control and Robotics, Las Vegas, (2002) . H.Zhang, J.Cao, W.Jiang, Controllability Criteria for Linear Fractional Differential Systems with State Delay and Impulses, Journal of Applied Mathematics, Article ID 146010, 1–9 pages (2013) . X-F.Zhou, J.Wei, L-GHub, Controllability of a fractional linear time-invariant neutral dynamical system , Applied Mathematics Letters, 26 ( 4 ), 418 – 424 ( 2013 ). X-F.Zhou, S.Liu and W.Jiang, Complete controllability of impulsive fractional linear timeinvariant systems with delay, Abstract and Applied Analysis, Article ID 374938, 1–7 pages (2013) .
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