Asymptotical stability of Riemann-Liouville fractional neutral systems

Abstract In this paper, the asymptotical stability of Riemann–Liouville fractional neutral systems is investigated. Applying Lyapunov direct method, we present new sufficient conditions on asymptotical stability in terms of linear matrix inequality (LMI) which can be easily solved. The advantage of our employed method is that one may directly calculate integer-order derivatives of the Lyapunov functions. Finally, two simple examples are given to show that the proposed method is computationally flexible and efficient.

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

[2]  Qiankun Song,et al.  Mittag-Leffler stability analysis of nonlinear fractional-order systems with impulses , 2017, Appl. Math. Comput..

[3]  Janusz Brzdek,et al.  On approximate solutions of some delayed fractional differential equations , 2016, Appl. Math. Lett..

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

[5]  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..

[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]  Yong Zhou,et al.  Existence of mild solutions for fractional neutral evolution equations , 2010, Comput. Math. Appl..

[8]  Yigang He,et al.  New results on stability and stabilization of a class of nonlinear fractional-order systems , 2013, Nonlinear Dynamics.

[9]  Wei Jiang,et al.  Asymptotical stability of Riemann-Liouville fractional singular systems with multiple time-varying delays , 2017, Appl. Math. Lett..

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

[11]  JinRong Wang,et al.  Finite time stability of fractional delay differential equations , 2017, Appl. Math. Lett..

[12]  Liping Chen,et al.  Finite-time stability criteria for a class of fractional-order neural networks with delay , 2015, Neural Computing and Applications.

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

[14]  Wei Jiang,et al.  Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks , 2016 .

[15]  Zhenhai Liu,et al.  Relaxation in nonconvex optimal control problems described by fractional differential equations , 2014 .

[16]  Wei Jiang,et al.  Asymptotical stability of Riemann–Liouville fractional nonlinear systems , 2016, Nonlinear Dynamics.

[17]  Vasily E. Tarasov,et al.  No violation of the Leibniz rule. No fractional derivative , 2013, Commun. Nonlinear Sci. Numer. Simul..

[18]  Shouming Zhong,et al.  Asymptotic stability analysis of fractional-order neutral systems with time delay , 2015 .

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

[20]  Jiqin Deng,et al.  Existence of solutions of initial value problems for nonlinear fractional differential equations , 2014, Appl. Math. Lett..

[21]  Wei Jiang,et al.  Lyapunov stability analysis of fractional nonlinear systems , 2016, Appl. Math. Lett..

[22]  Bo Yang,et al.  Positive solutions for a fractional boundary value problem , 2016, Appl. Math. Lett..

[23]  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 .