Stability and stabilization of a class of fractional-order nonlinear systems for 1

[1]  B. Onaral,et al.  Linear approximation of transfer function with a pole of fractional power , 1984 .

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

[3]  D. Kusnezov,et al.  Quantum Levy Processes and Fractional Kinetics , 1999, chao-dyn/9901002.

[4]  Yangquan Chen,et al.  Robust stability test of a class of linear time-invariant interval fractional-order system using Lyapunov inequality , 2007, Appl. Math. Comput..

[5]  D. Baleanu,et al.  Fractional Electromagnetic Equations Using Fractional Forms , 2009 .

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

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

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

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

[10]  Chuang Li,et al.  Robust stability and stabilization of fractional order interval systems with coupling relationships: The 0 , 2012, J. Frankl. Inst..

[11]  M. P. Aghababa Robust stabilization and synchronization of a class of fractional-order chaotic systems via a novel fractional sliding mode controller , 2012 .

[12]  Yong-Hong Lan,et al.  Observer-based robust control of a (1⩽ a ≪ 2) fractional-order uncertain systems: a linear matrix inequality approach , 2012 .

[13]  M. P. Aghababa A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems , 2013 .

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

[15]  Ningning Yang,et al.  A novel fractional-order hyperchaotic system stabilization via fractional sliding-mode control , 2013 .

[16]  Diyi Chen,et al.  Application of Takagi–Sugeno fuzzy model to a class of chaotic synchronization and anti-synchronization , 2013 .

[17]  Lorenz T. Biegler,et al.  Optimization of Fractional Order Dynamic Chemical Processing Systems , 2014 .

[18]  Bilal Senol,et al.  A numerical investigation for robust stability of fractional-order uncertain systems. , 2014, ISA transactions.

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

[20]  Yong Xu,et al.  Response of Fractional Oscillators With Viscoelastic Term Under Random Excitation , 2014 .

[21]  Zhe Gao,et al.  A computing method on stability intervals of time-delay for fractional-order retarded systems with commensurate time-delays , 2014, Autom..

[22]  Jinde Cao,et al.  Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays , 2014, Nonlinear Dynamics.

[23]  Xinzhi Liu,et al.  Fractional order Lyapunov stability theorem and its applications in synchronization of complex dynamical networks , 2014, Commun. Nonlinear Sci. Numer. Simul..

[24]  S. Ghasemi,et al.  Application of Fractional Calculus Theory to Robust Controller Design for Wind Turbine Generators , 2014, IEEE Transactions on Energy Conversion.

[25]  Yang Ge,et al.  Observer-based stabilisation of a class of fractional order non-linear systems for 0 α <;2 case , 2014 .

[26]  Ruoxun Zhang,et al.  Stability analysis of a class of fractional order nonlinear systems with order lying in (0, 2). , 2015, ISA transactions.

[27]  Baogui Xin,et al.  Finite-time stabilizing a fractional-order chaotic financial system with market confidence , 2015 .

[28]  Ying Yang,et al.  Robust Finite-Time Stability of Fractional Order Linear Time-Varying Impulsive Systems , 2015, Circuits Syst. Signal Process..

[29]  Diyi Chen,et al.  Modeling and stability analysis of a fractional-order Francis hydro-turbine governing system , 2015 .

[30]  Hao Zhang,et al.  Dynamic analysis and modeling of a novel fractional-order hydro-turbine-generator unit , 2015 .

[31]  Hao Zhang,et al.  The modeling of the fractional-order shafting system for a water jet mixed-flow pump during the startup process , 2015, Commun. Nonlinear Sci. Numer. Simul..

[32]  Zhe Gao,et al.  Robust stabilization criterion of fractional-order controllers for interval fractional-order plants , 2015, Autom..

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

[34]  Donglian Qi,et al.  Non-linear Mittag–Leffler stabilisation of commensurate fractional-order non-linear systems , 2015 .

[35]  P. Balasubramaniam,et al.  Approximate controllability of a class of fractional neutral stochastic integro-differential inclusions with infinite delay by using Mainardi's function , 2015, Appl. Math. Comput..

[36]  Bin Wang,et al.  Robust finite-time control of fractional-order nonlinear systems via frequency distributed model , 2016 .

[37]  M. Bettayeb,et al.  Design of sliding mode controllers for nonlinear fractional-order systems via diffusive representation , 2016 .

[38]  Bin Wang,et al.  Stabilization conditions for fuzzy control of uncertain fractional order non-linear systems with random disturbances , 2016 .

[39]  Mohammad Pourmahmood Aghababa,et al.  Control of non-integer-order dynamical systems using sliding mode scheme , 2016, Complex..

[40]  Sadegh Ebrahimkhani,et al.  Robust fractional order sliding mode control of doubly-fed induction generator (DFIG)-based wind turbines. , 2016, ISA transactions.

[41]  Yonghong Wu,et al.  Hamiltonian model and dynamic analyses for a hydro-turbine governing system with fractional item and time-lag , 2017, Commun. Nonlinear Sci. Numer. Simul..