Uniform stability of fractional neutral systems: a Lyapunov-Krasovskii functional approach

In this paper, we study the stability of nonlinear fractional neutral systems equipped with the Caputo derivative. We extend the Lyapunov-Krasovskii approach for the nonlinear fractional neutral systems. Conditions of uniform stability are obtained for the nonlinear fractional neutral systems.MSC:34K20, 34K37, 34K40.

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

[2]  Jiang Wei Finite-time Stability of Linear Fractional Order Neutral Systems , 2011 .

[3]  J. Hale,et al.  Stability of functional differential equations of neutral type , 1970 .

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

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

[6]  S. J. Sadati,et al.  Mittag-Leffler Stability Theorem for Fractional Nonlinear Systems with Delay , 2010 .

[7]  Margarita Rivero,et al.  Stability of Fractional Order Systems , 2013 .

[8]  K. Moore,et al.  Analytical Stability Bound for a Class of Delayed Fractional-Order Dynamic Systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[10]  Changpin Li,et al.  Asymptotical Stability of Nonlinear Fractional Differential System with Caputo Derivative , 2011 .

[11]  D. D. Perlmutter,et al.  Stability of time‐delay systems , 1972 .

[12]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[13]  Dumitru Baleanu,et al.  LYAPUNOV-KRASOVSKII STABILITY THEOREM FOR FRACTIONAL SYSTEMS WITH DELAY , 2011 .

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

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

[16]  Dumitru Baleanu,et al.  Razumikhin Stability Theorem for Fractional Systems with Delay , 2010 .

[17]  Aleksandar M. Spasic,et al.  Finite-time stability analysis of fractional order time-delay systems: Gronwall's approach , 2009, Math. Comput. Model..

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

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

[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]  Jack K. Hale,et al.  Introduction to Functional Differential Equations , 1993, Applied Mathematical Sciences.

[22]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

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

[24]  Shunian Zhang Unified stability theorem in RFDE and NFDE , 1990 .