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2013 | 23 | 3 | 491-500
Tytuł artykułu

Design of unknown input fractional-order observers for fractional-order systems

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper considers a method of designing fractional-order observers for continuous-time linear fractional-order systems with unknown inputs. Conditions for the existence of these observers are given. Sufficient conditions for the asymptotical stability of fractional-order observer errors with the fractional order α satisfying 0 < α < 2 are derived in terms of linear matrix inequalities. Two numerical examples are given to demonstrate the applicability of the proposed approach, where the fractional order α belongs to 1 ≤ α < 2 and 0 < α ≤ 1, respectively. A stability analysis of the fractional-order error system is made and it is shown that the fractional-order observers are as stable as their integer order counterpart and guarantee better convergence of the estimation error.
Rocznik
Tom
23
Numer
3
Strony
491-500
Opis fizyczny
Daty
wydano
2013
otrzymano
2012-06-15
poprawiono
2013-02-19
Twórcy
  • Faculty of Science, Technology and Communication (FSTC), University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg
  • Research Center for Automatic Control of Nancy (CRAN UMR, 7039, CNRS), University of Lorraine, IUT de Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France
autor
  • Faculty of Science, Technology and Communication (FSTC), University of Luxembourg, 6, rue Richard Coudenhove-Kalergi, L-1359 Luxembourg
  • Research Center for Automatic Control of Nancy (CRAN UMR, 7039, CNRS), University of Lorraine, IUT de Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France
Bibliografia
  • Bagley, R. and Calico, R. (1991). Fractional order state equations for the control of viscoelastically damped structures, Journal of Guidance, Control, and Dynamics 14(2): 304-311.
  • Ben-Israel, A. and Greville, T.N.E. (1974). Generalized Inverses: Theory and Applications, Wiley, New York, NY.
  • Boroujeni, E.A. and Momeni, H.R. (2012). Non-fragile nonlinear fractional order observer design for a class of nonlinear fractional order systems, Signal Processing 92(10): 2365-2370.
  • Boutayeb, M., Darouach, M. and Rafaralahy, H. (2002). Generalized state-space observers for chaotic synchronization and secure communication, IEEE Transactions on Circuits and Systems, I: Fundamental Theory and Applications 49(3): 345-349.
  • Caponetto, R., Dongola, G., Fortuna, L. and Petráš, I. (2010). Fractional Order Systems: Modeling and Control Applications, World Scientific Series on Nonlinear Science, Series A, World Scientific, Singapore.
  • Chen, Y., Ahn, H. and Podlubny, I. (2006). Robust stability check of fractional order linear time invariant systems with interval uncertainties, Signal Processing 86(10): 2611-2618.
  • Chen, Y., Vinagre, B.M. and Podlubny, I. (2004). Fractional order disturbance observer for robust vibration suppression, Nonlinear Dynamics 38(1): 355-367.
  • Chilali, M., Gahinet, P. and Apkarian, P. (1999). Robust pole placement in LMI regions, IEEE Transactions on Automatic Control 44(12): 2257-2270.
  • Dadras, S. and Momeni, H. (2011a). A new fractional order observer design for fractional order nonlinear systems, ASME 2011 International Design Engineering Technical Conference & Computers and Information in Engineering Conference, Washington, DC, USA, pp. 403-408.
  • Dadras, S. and Momeni, H.R. (2011b). Fractional sliding mode observer design for a class of uncertain fractional order nonlinear systems, IEEE Conference on Decision & Control, Orlando, FL, USA, pp. 6925-6930.
  • Darouach, M. (2000). Existence and design of functional observers for linear systems, IEEE Transactions on Automatic Control 45(5): 940-943.
  • Darouach, M., Zasadzinski, M. and Xu, S. (1994). Full-order observers for linear systems with unknown inputs, IEEE Transactions on Automatic Control 39(3): 606-609.
  • Delshad, S.S., Asheghan, M.M. and Beheshti, M.M. (2011). Synchronization of n-coupled incommensurate fractional-order chaotic systems with ring connection, Communications in Nonlinear Science and Numerical Simulation 16(9): 3815-3824.
  • Deng, W. (2007). Short memory principle and a predictor-corrector approach for fractional differential equations, Journal of Computational and Applied Mathematics 206(1): 174-188.
  • Dorckák, L. (1994). Numerical models for simulation the fractional-order control systems, Technical Report UEF04-94, Slovak Academy of Sciences, Kosice.
  • Engheta, N. (1996). On fractional calculus and fractional multipoles in electromagnetism, IEEE Transactions on Antennas and Propagation 44(4): 554-566.
  • Farges, C., Moze, M. and Sabatier, J. (2010). Pseudo-state feedback stabilization of commensurate fractional order systems, Automatica 46(10): 1730-1734.
  • Heaviside, O. (1971). Electromagnetic Theory, 3rd Edn., Chelsea Publishing Company, New York, NY.
  • Hilfer, R. (2001). Applications of Fractional Calculus in Physics, World Scientific Publishing, Singapore.
  • Kaczorek, T. (2011a). Selected Problems of Fractional Systems Theory, Lecture Notes in Control and Information Sciences, Vol. 411, Springer-Verlag, Berlin.
  • Kaczorek, T. (2011b). Singular fractional linear systems and electrical circuits, International Journal of Applied Mathematics and Computer Science 21(2): 379-384, DOI: 10.2478/v10006-011-0028-8.
  • Kilbas, A., Srivastava, H. and Trujillo, J. (2006). Theory and Applications of Fractional Differential Equations, North-Holland Mathematics Studies, Vol. 204, Elsevier, Amsterdam.
  • Lancaster, P. and Tismenetsky, M. (1985). The Theory of Matrices, 2nd Edn., Academic Press, Orlando, FL.
  • Lu, J. and Chen, Y. (2010). Robust stability and stabilization of fractional-order interval systems with the fractional-order α: The 0 < α < 1 case, IEEE Transactions on Automatic Control 55(1): 152-158.
  • Matignon, D. (1996). Stability results for fractional differential equations with applications to control processing, IEEE International Conference on Systems, Man, Cybernetics, Lille, France, pp. 963-968.
  • Matignon, D. (1998). Generalized fractional differential and difference equations: Stability properties and modelling issues, Mathematical Theory of Networks and Systems Symposium, Padova, Italy, pp. 503-506.
  • Matignon, D. and Andréa-Novel, B. (1996). Some results on controllability and observability of finite-dimensional fractional differential systems, Mathematical Theory of Networks and Systems Symposium, Lille, France, pp. 952-956.
  • Matignon, D. and Andréa-Novel, B. (1997). Observer-based for fractional differential systems, IEEE Conference on Decision and Control, San Diego, CA, USA, pp. 4967-4972.
  • Monje, C.A., Chen, Y.Q., Vinagre, B.M., Xue, D. and Feliu, V. (2010). Fractional-order Systems and Controls: Fundamentals and Applications, Springer, Berlin.
  • Petráš, I. (2010). A note on the fractional-order Volta system, Communications in Nonlinear Science and Numerical Simulation 15(2): 384-393.
  • Petráš, I. (2011). Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation, Springer, Berlin.
  • Petráš, I., Chen, Y. and Vinagre, B. (2004). Robust stability test for interval fractional-order linear systems, in V. Blondel and A. Megretski (Eds.), Unsolved Problems in the Mathematics of Systems and Control, Vol. 38, Princeton University Press, Princeton, NJ, pp. 208-210.
  • Podlubny, I. (1999). Fractional Differential Equations, Academic, New York, NY.
  • Podlubny, I. (2002). Geometric and physical interpretation of fractional integration and fractional differentiation, Fractional Calculus & Applied Analysis 5(4): 367-386.
  • Rao, C. and Mitra, S. (1971). Generalized Inverse of Matrices and Its Applications, Wiley, New York, NY.
  • Rossikhin, Y. and Shitikova, M. (1997). Application of fractional derivatives to the analysis of damped vibrations of viscoelastic single mass system, Acta Mechanica 120(109): 109-125.
  • Sabatier, J., Farges, C., Merveillaut, M. and Feneteau, L. (2012). On observability and pseudo state estimation of fractional order systems, European Journal of Control 18(3): 260-271.
  • Sabatier, J., Moze, M. and Farges, C. (2008). On stability of fractional order systems, IFAC Workshop on Fractional Differentiation and Its Application, Ankara, Turkey.
  • Sabatier, J., Moze, M. and Farges, C. (2010). LMI conditions for fractional order systems, Computers & Mathematics with Applications 59(5): 1594-1609.
  • Sun, H., Abdelwahad, A. and Onaral, B. (1984). Linear approximation of transfer function with a pole of fractional order, IEEE Transactions on Automatic Control 29(5): 441-444.
  • Trigeassou, J., Maamri, N., Sabatier, J. and Oustaloup, A. (2011). A Lyapunov approach to the stability of fractional differential equations, Signal Processing 91(3): 437-445.
  • Trinh, H. and Fernando, T. (2012). Functional Observers for Dynamical Systems, Lecture Notes in Control and Information Sciences, Vol. 420, Springer, Berlin.
  • Tsui, C. (1985). A new algorithm for the design of multifunctional observers, IEEE Transactions on Automatic Control 30(1): 89-93.
  • Van Dooren, P. (1984). Reduced-order observers: A new algorithm and proof, Systems & Control Letters 4(5): 243-251.
  • Watson, J. and Grigoriadis, K. (1998). Optimal unbiased filtering via linear matrix inequalities, Systems & Control Letters 35(2): 111-118.
Typ dokumentu
Bibliografia
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