Stability of fractional-order switched non-linear systems

This study addresses the stability issue of a class of fractional-order switched non-linear systems. A general stability condition is established based on which two new concepts named Mittag-Leffler increment and average Mittag-Leffler increment are proposed and two alternative stability conditions are obtained. These conditions fully reveal the trade-off between each subsystem's dynamics, and the value of the fractional order. The new results are further applied to a class of fractional-order multi-agent systems with switching cooperative control laws.

[1]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[2]  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 .

[3]  José António Tenreiro Machado,et al.  On the numerical computation of the Mittag-Leffler function , 2014, Commun. Nonlinear Sci. Numer. Simul..

[4]  Zhengrong Xiang,et al.  Robust control for uncertain switched non-linear systems with time delay under asynchronous switching , 2009 .

[5]  Min Shi,et al.  A Modified Multi-Step Differential Transform Method for Solving Fractional Dynamic Systems , 2013 .

[6]  Jun Zhao,et al.  On stability, L2-gain and Hinfinity control for switched systems , 2008, Autom..

[7]  Jun Zhao,et al.  Variable structure control method to the output tracking control of cascade non-linear switched systems , 2009 .

[8]  Peng Shi,et al.  Stability and Stabilization of Switched Linear Systems With Mode-Dependent Average Dwell Time , 2012, IEEE Transactions on Automatic Control.

[9]  Bin Jiang,et al.  On stabilization of switched nonlinear systems with unstable modes , 2009, Syst. Control. Lett..

[10]  K.N. Salama,et al.  Control and switching synchronization of fractional order chaotic systems using active control technique , 2013, Journal of advanced research.

[11]  Ali Khaki Sedigh,et al.  Sufficient condition for stabilization of linear time invariant fractional order switched systems and variable structure control stabilizers. , 2012, ISA transactions.

[12]  Yongcan Cao,et al.  Distributed Coordination of Networked Fractional-Order Systems , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Jimin Yu,et al.  Generalized Mittag-Leffler stability of multi-variables fractional order nonlinear systems , 2013, Autom..

[14]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.

[15]  Ligang Wu,et al.  Sliding Mode Control of Uncertain Parameter-Switching Hybrid Systems , 2014 .

[16]  Hengjun Zhang,et al.  Robust Practical Stabilization of Nonholonomic Mobile Robots Based on Visual Servoing Feedback with Inputs Saturation , 2014 .

[17]  Karolin Papst,et al.  Stability Theory Of Switched Dynamical Systems , 2016 .

[18]  Zhiyong Yu,et al.  Leader-following consensus of fractional-order multi-agent systems under fixed topology , 2015, Neurocomputing.

[19]  S. Leela,et al.  LYAPUNOV THEORY FOR FRACTIONAL DIFFERENTIAL EQUATIONS , 2008 .

[20]  Inés Tejado,et al.  Stability of fractional order switching systems , 2012, Comput. Math. Appl..

[21]  Liping Chen,et al.  Stability and Stabilization of a Class of Nonlinear Fractional-Order Systems With Caputo Derivative , 2012, IEEE Transactions on Circuits and Systems II: Express Briefs.

[22]  Yongcan Cao,et al.  Distributed formation control for fractional-order systems: Dynamic interaction and absolute/relative damping , 2010, Syst. Control. Lett..

[23]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[24]  Hua Chen,et al.  Global Practical Stabilization for Non-holonomic Mobile Robots with Uncalibrated Visual Parameters by Using a Switching Controller , 2013, IMA J. Math. Control. Inf..

[25]  Hua Chen,et al.  Robust stabilization for a class of dynamic feedback uncertain nonholonomic mobile robots with input saturation , 2014 .

[26]  Mohammad Saleh Tavazoei,et al.  Chaos generation via a switching fractional multi-model system , 2010 .

[27]  Igor Podlubny,et al.  Mittag-Leffler stability of fractional order nonlinear dynamic systems , 2009, Autom..

[28]  Harry Pollard,et al.  The completely monotonic character of the Mittag-Leffler function $E_a \left( { - x} \right)$ , 1948 .

[29]  Jun Zhao,et al.  On stability, L 2 -gain and H 8 control for switched systems , 2008 .

[30]  Changpin Li,et al.  A survey on the stability of fractional differential equations , 2011 .