State Feedback Control for Fractional Differential Systems with Riemann-Liouville Derivative

Yuan Fang

doi:10.4028/www.scientific.net/AMR.562-564.2053

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HomeAdvanced Materials ResearchAdvanced Materials Research Vols. 562-564State Feedback Control for Fractional Differential...

State Feedback Control for Fractional Differential Systems with Riemann-Liouville Derivative

Abstract:

This paper studies state feedback control for fractional differential systems with Riemann-Lιiouville derivative, which matrix A not satisfying the condition ιarg(λ(A))ι>α/2 . Based on the state feedback controllers’ designer, and Linear Matrix Inequality (LMI) apαproach, sufficient conditions for the systems with fraction order α (0<α<1) and α (1≤α<2) obtained respectively.

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Periodical:

Advanced Materials Research (Volumes 562-564)

Pages:

2053-2056

DOI:

https://doi.org/10.4028/www.scientific.net/AMR.562-564.2053

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Online since:

August 2012

Authors:

Yuan Fang

Keywords:

Feedback Control, Linear Matrix Inequality (LMI), Riemann-Liouville Derivative, Stability

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References

[1] Ahn H S, Chen Y Q. Necessary and sufficient stability condition of fractional-order interval linear systems[J]. Automatica, 2008, 44: 2985-2988.

DOI: 10.1016/j.automatica.2008.07.003

Google Scholar

[2] Li Y, Chen Y Q, Podlubny I. Mittag-Leffler stability of fractional order nonlinear dynamic systems[J]. Automatica, 2009, 45: 1965-(1969).

DOI: 10.1016/j.automatica.2009.04.003

Google Scholar

[3] Li Y, Chen Y Q, Podlubny I. Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability[J]. Computers and Mathematics with Applications, 2010, 59: 1810-1821.

DOI: 10.1016/j.camwa.2009.08.019

Google Scholar

[4] Qian D L, Li C P, Agarwal R P, Wong P J Y. Stability analysis of fractional differential system with Riemann-Liouville derivative[J]. Mathematical and Computer Modelling, 2010, 52: 862-874.

DOI: 10.1016/j.mcm.2010.05.016

Google Scholar

[5] Trigeassou J C, Maamri N, Sabatier J, Oustaloup A. A Lyapunov approach to the stability of fractional differential equations[J]. Signal Processing, 2011, 91: 437-445.

DOI: 10.1016/j.sigpro.2010.04.024

Google Scholar

[6] Sabatier J, Moze M, Farges C. LMI stability conditions for fractional order systems[J]. Computers and Mathematics with Applications, 2010, 59: 1594-1609.

DOI: 10.1016/j.camwa.2009.08.003

Google Scholar

[7] Lan Y H, Zhou Y. LMI-based robust control of fractional-order uncertain linear systems[J]. Computers and Mathematics with Applications(2011), doi: 10. 1016/j. camwa. 2011. 03. 028.

DOI: 10.1016/j.camwa.2011.03.028

Google Scholar

[8] Ahn H S, Chen Y Q, Podlubny I. Robust stability test of a class of linear time-invariant interval fractional-order system usting Lyapunov inequality[J]. Applied Matehmatics and Computation, 2007, 187: 27-34.

DOI: 10.1016/j.amc.2006.08.099

Google Scholar

[9] Chen Y Q, Ahn H S, Podlubny I. Robust stability check of fractional order linear time invariant systems with interval uncertainties[J]. Signal Processing, 2006, 86: 2611-2618.

DOI: 10.1016/j.sigpro.2006.02.011

Google Scholar

[10] Chilali M, Gahinet P, Apkarian P. Robust pole placement in LMI regions, IEEE Transtctions on Automatic Control, 1999, 44(12): 2257-2270.

DOI: 10.1109/9.811208

Google Scholar

[11] Chai L, Fei S M, Xin Y B. A new type of adaptive control for time-delay systems with input delay[J], Journal of systems science and Mathematical Sciences, 2008, 28(12): 1535-1544.

Google Scholar