Robust output feedback control for fractional order nonlinear systems with time-varying delays

Robust controller design problem is investigated for a class of fractional order nonlinear systems with time varying delays. Firstly, a reduced-order observer is designed. Then, an output feedback controller is designed. Both the designed observer and controller are independent of time delays. By choosing appropriate Lyapunov functions, we prove the designed controller can render the fractional order system asymptotically stable. A simulation example is given to verify the effectiveness of the proposed approach.

[1]  D. Baleanu,et al.  Stability analysis of Caputo fractional-order nonlinear systems revisited , 2011, Nonlinear Dynamics.

[2]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach , 2009, IEEE Transactions on Automatic Control.

[3]  Shu Liang,et al.  A novel algorithm on adaptive backstepping control of fractional order systems , 2015, Neurocomputing.

[4]  Changpin Li,et al.  Stability Analysis of Fractional Differential Systems with Order Lying in (1, 2) , 2011 .

[5]  V. Lakshmikantham,et al.  Theory of Fractional Dynamic Systems , 2009 .

[6]  V. Lakshmikantham,et al.  Basic theory of fractional differential equations , 2008 .

[7]  K. Diethelm The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type , 2010 .

[8]  Jun-Guo Lu,et al.  Stability Analysis of a Class of Nonlinear Fractional-Order Systems , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  D. Matignon Stability results for fractional differential equations with applications to control processing , 1996 .

[10]  I. Podlubny Fractional differential equations , 1998 .

[11]  Li Xu,et al.  Adaptive Mittag-Leffler stabilization of commensurate fractional-order nonlinear systems , 2014, 53rd IEEE Conference on Decision and Control.

[12]  Tianzeng Li,et al.  Stability Analysis of Fractional-Order Nonlinear Systems with Delay , 2014 .

[13]  Young-Hun Lim,et al.  Stability and Stabilization of Fractional-Order Linear Systems Subject to Input Saturation , 2013, IEEE Transactions on Automatic Control.

[14]  J. Partington,et al.  Coprime factorizations and stability of fractional differential systems , 2000 .

[15]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies) , 2006 .

[16]  Saptarshi Das,et al.  Intelligent Fractional Order Systems and Control - An Introduction , 2012, Studies in Computational Intelligence.

[17]  Jun-Guo Lu,et al.  Robust Stability and Stabilization of Fractional-Order Interval Systems with the Fractional Order $\alpha$: The $0≪\alpha≪1$ Case , 2010, IEEE Transactions on Automatic Control.

[18]  Song Liu,et al.  Lyapunov method for nonlinear fractional differential systems with delay , 2015 .

[19]  Peng Shi,et al.  Robust backstepping control for a class of time delayed systems , 2005, IEEE Transactions on Automatic Control.

[20]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[21]  Grzegorz Litak,et al.  Chaotic vibrations of the duffing system with fractional damping. , 2014, Chaos.

[22]  Manuel A. Duarte-Mermoud,et al.  Lyapunov functions for fractional order systems , 2014, Commun. Nonlinear Sci. Numer. Simul..

[23]  Jinhu Lü,et al.  Stability analysis of linear fractional differential system with multiple time delays , 2007 .

[24]  Mohammad Saleh Tavazoei,et al.  Stability criteria for a class of fractional order systems , 2010 .

[25]  Gang Feng,et al.  Asymptotical stabilization of fractional-order linear systems in triangular form , 2013, Autom..