Open Science Research Excellence

Open Science Index

Commenced in January 2007 Frequency: Monthly Edition: International Publications Count: 29640

Select areas to restrict search in scientific publication database:
Observer Based Control of a Class of Nonlinear Fractional Order Systems using LMI
Design of an observer based controller for a class of fractional order systems has been done. Fractional order mathematics is used to express the system and the proposed observer. Fractional order Lyapunov theorem is used to derive the closed-loop asymptotic stability. The gains of the observer and observer based controller are derived systematically using the linear matrix inequality approach. Finally, the simulation results demonstrate validity and effectiveness of the proposed observer based controller.
Digital Object Identifier (DOI):


[1] C. A. Monje , Y. Q. Chen, B.M. Vinagre, D. Xue, and V. Feliu, Fractional-order Systems and Controls: Fundamentals and Applications, New York, Springer, 2010.
[2] A. A. Kilbas, H. M. Srivastava and J. J.Trujillo , Theory and applications of fractional differential equations, Amsterdam, The Netherlands: Elsevier, 2006.
[3] R. Hilfer , Application of fractional calculus in physics, New Jersey: World Scientific, 2001.
[4] S. Dadras, and H.R.Momeni, "Control of a fractional-order economical system via sliding mode, " Physica A, Vol.389, No. 12, pp. 2434-2442, 2010.
[5] I. Podlubny,"Fractional-order systems and PIλD╬╝ controller,"IEEE Trans. Automat. Control, Vol.44, No. 1, pp. 208-214, 1999.
[6] D. Matignon, "Stability results for fractional differential equations with applications to control processing," in: Computational Engineering in Systems Applications, Lille, France, IMACS, IEEE-SMC, vol. 2, pp.963-968, July, 1996.
[7] I. N-doye, M. Zasadzinski, M. Darouach and N. E. Radhy, "Observer- Based Control for Fractional-Order Continuous-time Systems," Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, China, December 2009, pp.1932-1937.
[8] J. G. Lu, Nonlinear observer design to synchronize fractional-order chaotic systems via a scalar transmitted signal, Physica A. Vol.359, pp. 107-118, 2006.
[9] L. Xinjie, L. Jie, D. Pengzhen, X. Lifen, Observer Designing for Generalized Synchronization of Fractional Order Hyper-chaotic Lu System, in 2009 proc of Chinese Control and Decision Conference. pp. 426-431.
[10] M. S. Tavazoei, and M. Haeri, Synchronization of chaotic fractionalorder systems via active sliding mode controller, Physica A. Vol. 387, pp.57-70, 2008.
[11] M. M. Asheghan, M. T. Hamidi Beheshti, M. S. Tavazoei, Robust synchronization of perturbed Chen-s fractional-order chaotic systems, Commun Nonlinear Sci Numer Simulat. Vol.16, pp.1044-1051, 2011.
[12] Y. Li, Y. Q. Chen, I. Podlubny, Mittag-Leffler stability of fractional order nonlinear dynamic systems, Automatica. Vol.45, pp.1965-1969, 2006.
[13] J.C. Trigeassou, N.Maamri, J.Sabatier, A.Oustaloup, A Lyapunov approach to the stability of fractional differential equations, Signal Process. Vol.91, pp.437-445, 2011.
[14] I. Podlubny, Fractional differential equations. Academic Press, New York, 1999.
[15] M.O. Efe, Fractional Fuzzy Adaptive Sliding-Mode Control of a 2-DOF Direct-Drive Robot Arm, IEEE T SYST MAN CY B. Vol.38, pp.1561- 1570, 2008.
[16] S. Boyd, L.E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, 1994.
[17] M. Pourgholi, V. Johari Majd, A Nonlinear Adaptive Resilient Observer Design for a Class of Lipschitz Systems Using LMI, Circuits Syst Signal Process, Vol.30, pp.1401-1415, 2011.
[18] Y. Li, Y. Q. Chen, I. Podlubny, Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag_Leffler stability, Comput Math APPL. Vol.59, pp.1810-1821, 2010.
[19] D. Valério, "Ninteger v. 2.3, Fractional control toolbox for MatLab, Fractional derivatives and applications," Universidadetecnica de lisboainstituto superior tecnico, 2005.
Vol:13 No:05 2019Vol:13 No:04 2019Vol:13 No:03 2019Vol:13 No:02 2019Vol:13 No:01 2019
Vol:12 No:12 2018Vol:12 No:11 2018Vol:12 No:10 2018Vol:12 No:09 2018Vol:12 No:08 2018Vol:12 No:07 2018Vol:12 No:06 2018Vol:12 No:05 2018Vol:12 No:04 2018Vol:12 No:03 2018Vol:12 No:02 2018Vol:12 No:01 2018
Vol:11 No:12 2017Vol:11 No:11 2017Vol:11 No:10 2017Vol:11 No:09 2017Vol:11 No:08 2017Vol:11 No:07 2017Vol:11 No:06 2017Vol:11 No:05 2017Vol:11 No:04 2017Vol:11 No:03 2017Vol:11 No:02 2017Vol:11 No:01 2017
Vol:10 No:12 2016Vol:10 No:11 2016Vol:10 No:10 2016Vol:10 No:09 2016Vol:10 No:08 2016Vol:10 No:07 2016Vol:10 No:06 2016Vol:10 No:05 2016Vol:10 No:04 2016Vol:10 No:03 2016Vol:10 No:02 2016Vol:10 No:01 2016
Vol:9 No:12 2015Vol:9 No:11 2015Vol:9 No:10 2015Vol:9 No:09 2015Vol:9 No:08 2015Vol:9 No:07 2015Vol:9 No:06 2015Vol:9 No:05 2015Vol:9 No:04 2015Vol:9 No:03 2015Vol:9 No:02 2015Vol:9 No:01 2015
Vol:8 No:12 2014Vol:8 No:11 2014Vol:8 No:10 2014Vol:8 No:09 2014Vol:8 No:08 2014Vol:8 No:07 2014Vol:8 No:06 2014Vol:8 No:05 2014Vol:8 No:04 2014Vol:8 No:03 2014Vol:8 No:02 2014Vol:8 No:01 2014
Vol:7 No:12 2013Vol:7 No:11 2013Vol:7 No:10 2013Vol:7 No:09 2013Vol:7 No:08 2013Vol:7 No:07 2013Vol:7 No:06 2013Vol:7 No:05 2013Vol:7 No:04 2013Vol:7 No:03 2013Vol:7 No:02 2013Vol:7 No:01 2013
Vol:6 No:12 2012Vol:6 No:11 2012Vol:6 No:10 2012Vol:6 No:09 2012Vol:6 No:08 2012Vol:6 No:07 2012Vol:6 No:06 2012Vol:6 No:05 2012Vol:6 No:04 2012Vol:6 No:03 2012Vol:6 No:02 2012Vol:6 No:01 2012
Vol:5 No:12 2011Vol:5 No:11 2011Vol:5 No:10 2011Vol:5 No:09 2011Vol:5 No:08 2011Vol:5 No:07 2011Vol:5 No:06 2011Vol:5 No:05 2011Vol:5 No:04 2011Vol:5 No:03 2011Vol:5 No:02 2011Vol:5 No:01 2011
Vol:4 No:12 2010Vol:4 No:11 2010Vol:4 No:10 2010Vol:4 No:09 2010Vol:4 No:08 2010Vol:4 No:07 2010Vol:4 No:06 2010Vol:4 No:05 2010Vol:4 No:04 2010Vol:4 No:03 2010Vol:4 No:02 2010Vol:4 No:01 2010
Vol:3 No:12 2009Vol:3 No:11 2009Vol:3 No:10 2009Vol:3 No:09 2009Vol:3 No:08 2009Vol:3 No:07 2009Vol:3 No:06 2009Vol:3 No:05 2009Vol:3 No:04 2009Vol:3 No:03 2009Vol:3 No:02 2009Vol:3 No:01 2009
Vol:2 No:12 2008Vol:2 No:11 2008Vol:2 No:10 2008Vol:2 No:09 2008Vol:2 No:08 2008Vol:2 No:07 2008Vol:2 No:06 2008Vol:2 No:05 2008Vol:2 No:04 2008Vol:2 No:03 2008Vol:2 No:02 2008Vol:2 No:01 2008
Vol:1 No:12 2007Vol:1 No:11 2007Vol:1 No:10 2007Vol:1 No:09 2007Vol:1 No:08 2007Vol:1 No:07 2007Vol:1 No:06 2007Vol:1 No:05 2007Vol:1 No:04 2007Vol:1 No:03 2007Vol:1 No:02 2007Vol:1 No:01 2007