Stability analysis of a class of nonlinear fractional‐order systems under control input saturation

[1]  D. O’Regan,et al.  Lyapunov functions and strict stability of Caputo fractional differential equations , 2015 .

[2]  Elena Grigorenko,et al.  Chaotic dynamics of the fractional Lorenz system. , 2003, Physical review letters.

[3]  Kia Fallahi,et al.  An application of Chen system for secure chaotic communication based on extended Kalman filter and multi-shift cipher algorithm , 2008 .

[4]  Naveen Eluru,et al.  Modeling vehicle operating speed on urban roads in Montreal: a panel mixed ordered probit fractional split model. , 2013, Accident; analysis and prevention.

[5]  S. Bhalekar,et al.  Chaos in fractional order financial delay system , 2016 .

[6]  José António Tenreiro Machado,et al.  An extension of estimation of domain of attraction for fractional order linear system subject to saturation control , 2015, Appl. Math. Lett..

[7]  Alessandro Pisano,et al.  On the sliding‐mode control of fractional‐order nonlinear uncertain dynamics , 2016 .

[8]  Chunguang Li,et al.  Chaos in the fractional order Chen system and its control , 2004 .

[9]  Esmat Sadat Alaviyan Shahri,et al.  Stabilization of Fractional-Order Systems Subject to Saturation Element Using Fractional Dynamic Output Feedback Sliding Mode Control , 2017 .

[10]  Esmat Sadat Alaviyan Shahri,et al.  An analysis and design method for fractional‐order linear systems subject to actuator saturation and disturbance , 2016 .

[11]  Manuel A. Duarte-Mermoud,et al.  On the Lyapunov theory for fractional order systems , 2016, Appl. Math. Comput..

[12]  Richard L. Magin,et al.  Chaos in the fractional order nonlinear Bloch equation with delay , 2015, Commun. Nonlinear Sci. Numer. Simul..

[13]  J. A. Tenreiro Machado,et al.  Dynamic stability analysis of fractional order leaky integrator echo state neural networks , 2017, Commun. Nonlinear Sci. Numer. Simul..

[14]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[15]  Yangquan Chen,et al.  Fractional calculus in image processing: a review , 2016, ArXiv.

[16]  Esmat Sadat Alaviyan Shahri,et al.  A Stability Analysis on Fractional Order Linear System with Nonlinear Saturated Disturbance , 2015 .

[17]  Ping Zhou,et al.  Stabilization of a fractional-order chaotic brushless DC motor via a single input , 2015 .

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

[19]  M. Darouach,et al.  Exponential stabilization of a class of nonlinear systems: A generalized GronwallBellman lemma appr , 2011 .

[20]  Ravi P. Agarwal,et al.  Stability analysis of fractional differential system with Riemann-Liouville derivative , 2010, Math. Comput. Model..

[21]  Bo Zhang,et al.  Global exponential stabilization for chaotic brushless DC motors with a single input , 2014 .

[22]  Saber Naseri,et al.  Comment on "A Strong Convergence of a Generalized Iterative Method for Semigroups of Nonexpansive Mappings in Hilbert Spaces" , 2011 .

[23]  Tingshu Hu,et al.  An analysis and design method for linear systems subject to actuator saturation and disturbance , 2002, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[24]  Mohamed Darouach,et al.  On the robustness of linear and non-linear fractional-order systems with non-linear uncertain parameters , 2016, IMA J. Math. Control. Inf..

[25]  Yong-sheng Ding,et al.  A generalized Gronwall inequality and its application to a fractional differential equation , 2007 .

[26]  C. F. Lorenzo,et al.  Chaos in a fractional order Chua's system , 1995 .

[27]  Sundarapandian Vaidyanathan,et al.  Dynamic analysis and chaos suppression in a fractional order brushless DC motor , 2017 .

[28]  Manuel A. Duarte-Mermoud,et al.  Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems , 2015, Commun. Nonlinear Sci. Numer. Simul..

[29]  M. Rivero,et al.  Fractional calculus: A survey of useful formulas , 2013, The European Physical Journal Special Topics.

[30]  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.

[31]  Bin Wang,et al.  Stabilization of a Fractional-Order Nonlinear Brushless Direct Current Motor , 2017 .

[32]  M. De la Sen,et al.  About Robust Stability of Caputo Linear Fractional Dynamic Systems with Time Delays through Fixed Point Theory , 2011 .

[33]  Chunguang Li,et al.  Chaos and hyperchaos in the fractional-order Rössler equations , 2004 .

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

[35]  Todd J. Freeborn,et al.  A Survey of Fractional-Order Circuit Models for Biology and Biomedicine , 2013, IEEE Journal on Emerging and Selected Topics in Circuits and Systems.

[36]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[37]  O. Agrawal,et al.  Advances in Fractional Calculus , 2007 .

[38]  Rafael Vieira de Sousa,et al.  Fractional PID controller in an active image stabilization system for mitigating vibration effects in agricultural tractors , 2016, Comput. Electron. Agric..